Numbers whose binary and ternary digit sums are prime: Difference between revisions

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Line 2: ;Task: Show positive integers   '''n'''   whose binary and ternary digits sum are prime,   where   '''n <  <   200'''. <br><br> =={{header\|11l}}== {{trans\|Nim}} <syntaxhighlight lang="11l">F is_prime(a) I a == 2 R 1B I a < 2 \| a % 2 == 0 R 0B L(i) (3 .. Int(sqrt(a))).step(2) I a % i == 0 R 0B R 1B F digit_sum(=n, b) V result = 0 L n != 0 result += n % b n I/= b R result V count = 0 L(n) 2..199 I is_prime(digit_sum(n, 2)) & is_prime(digit_sum(n, 3)) count++ print(‘#3’.format(n), end' I count % 16 == 0 {"\n"} E ‘ ’) print() print(‘Found ’count‘ numbers.’)</syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Found 61 numbers. </pre> =={{header\|Action!}}== {{libheader\|Action! Sieve of Eratosthenes}} <syntaxhighlight lang="action!">INCLUDE "H6:SIEVE.ACT" BYTE Func IsPrime(INT i BYTE base BYTE ARRAY primes) BYTE sum,d sum=0 WHILE i#0 DO d=i MOD base sum==+d i==/base OD RETURN (primes(sum)) PROC Main() DEFINE MAX="199" BYTE ARRAY primes(MAX+1) INT i,count=[0] Put(125) PutE() ;clear the screen Sieve(primes,MAX+1) FOR i=1 TO MAX DO IF IsPrime(i,2,primes)=1 AND IsPrime(i,3,primes)=1 THEN PrintI(i) Put(32) count==+1 FI OD PrintF("%E%EThere are %I numbers",count) RETURN</syntaxhighlight> {{out}} [https://gitlab.com/amarok8bit/action-rosetta-code/-/raw/master/images/Numbers_which_binary_and_ternary_digit_sum_are_prime.png Screenshot from Atari 8-bit computer] <pre> 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 14 5 151 155 157 162 167 171 173 179 181 185 191 193 199 There are 61 numbers </pre> =={{header\|ALGOL 68}}== {{libheader\|ALGOL 68-primes}} ~~<lang algol68>BEGIN # find numbers whose digit sums in binary and ternary are prime #~~ <syntaxhighlight lang="algol68">BEGIN # find numbers whose digit sums in binary and ternary are prime # ~~# reurns a sieve of primes up to n #~~ ~~PROC sieve = ( INT n )[]BOOL:~~ ~~BEGIN~~ ~~[ 1 : n ]BOOL p;~~ ~~p[ 1 ] := FALSE; p[ 2 ] := TRUE;~~ ~~FOR i FROM 3 BY 2 TO n DO p[ i ] := TRUE OD;~~ ~~FOR i FROM 4 BY 2 TO n DO p[ i ] := FALSE OD;~~ ~~FOR i FROM 3 BY 2 TO ENTIER sqrt( n ) DO~~ ~~IF p[ i ] THEN FOR s FROM i * i BY i + i TO n DO p[ s ] := FALSE OD FI~~ ~~OD;~~ p ~~END # prime list # ;~~ # returns the digit sum of n in base b # PRIO DIGITSUM = 9; Line 32 ⟶ 100: END # DIGITSUM # ; INT max number = 200; PR read "primes.incl.a68" PR ~~[]BOOL prime = sieve( max number );~~ []BOOL prime = PRIMESIEVE 200; INT n count := 0; FOR n TO ~~max~~UPB ~~number~~prime DO INT d sum 2 = n DIGITSUM 2; IF prime[ d sum 2 ] THEN Line 49 ⟶ 118: print( ( "Found ", whole( n count, 0 ), " numbers whose binary and ternary digit sums are prime", newline ) ); print( ( " those that are themselves prime are suffixed with a """"", newline ) ) END</~~lang~~syntaxhighlight> {{out}} <pre> Line 62 ⟶ 131: =={{header\|ALGOL-M}}== <~~lang~~syntaxhighlight lang="algolm">begin integer function mod(a,b); integer a,b; Line 98 ⟶ 167: end; end; end</~~lang~~syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 Line 109 ⟶ 178: =={{header\|ALGOL W}}== <~~lang~~syntaxhighlight lang="algolw">begin % find numbers whose binary and ternary digit sums are prime % % returns the digit sum of n in base b % integer procedure digitSum( integer value n, base ) ; Line 147 ⟶ 216: write( i_w := 1, s_w := 0, "Found ", nCount, " numbers with prime binary and ternary digit sums up to ", MAX_PRIME ) end end.</~~lang~~syntaxhighlight> {{out}} <pre> Line 160 ⟶ 229: =={{header\|APL}}== {{works with\|Dyalog APL}} <~~lang~~syntaxhighlight ~~APL~~lang="apl">(⊢(/⍨)(∧/((2=0+.=⍳\|⊢)¨2 3(+/⊥⍣¯1)¨⊢))¨) ⍳200</~~lang~~syntaxhighlight> {{out}} <pre>5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 Line 167 ⟶ 236: =={{header\|Arturo}}== <~~lang~~syntaxhighlight lang="rebol">loop split.every: 10 select 1..199 'n [ and? prime? sum digits.base: 2 n prime? sum digits.base: 3 n ] 'a -> print map a => [pad to :string & 4]</~~lang~~syntaxhighlight> {{out}} Line 182 ⟶ 251: 199</pre> =={{header\|AWK}}== <syntaxhighlight lang="awk"> ~~<lang AWK>~~ # syntax: GAWK -f NUMBERS_WHICH_BINARY_AND_TERNARY_DIGIT_SUM_ARE_PRIME.AWK # converted from C Line 213 ⟶ 282: return(1) } </syntaxhighlight> ~~</lang>~~ {{out}} <pre> Line 227 ⟶ 296: =={{header\|BASIC}}== ==={{header\|Chipmunk Basic}}=== ~~None of the digit sums are higher than 9, so the easiest thing to do~~ {{trans\|GW-BASIC}} ~~is to hardcode which ones are prime.~~ <syntaxhighlight lang="basic"> 100 rem Numbers which binary and ternary digit sum are prime 110 for n = 2 to 199 120 if is_prime(digit_sum(n,2)) <> 0 then 130 if is_prime(digit_sum(n,3)) <> 0 then print using "### ";n; 140 endif 150 next n 160 print 170 end 180 sub is_prime(p) 190 if p = 3 or p = 2 then 200 is_prime = 1 210 else 220 if p = 1 then 230 is_prime = 0 240 else 250 q = 1 : i = 1 260 i = i+1 270 if p mod i = 0 then q = 0 280 if ii <= p and q <> 0 then 260 290 is_prime = q 300 endif 310 endif 320 end sub 330 sub digit_sum(n,bas) 340 p = 0 : xn = n 350 while xn <> 0 360 p = p+xn mod bas 370 xn = int(xn/bas) 380 wend 390 digit_sum = p 400 end sub </syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 </pre> ==={{header\|FreeBASIC}}=== <syntaxhighlight lang="freebasic">#include"isprime.bas" function digsum( byval n as uinteger, b as const uinteger ) as uinteger 'finds the digit sum of n in base b dim as uinteger sum = 0 while n sum+=n mod b n\=b wend return sum end function for n as uinteger = 1 to 200 if isprime(digsum(n,2)) and isprime(digsum(n,3)) then print n;" "; next n : print</syntaxhighlight> {{out}}<pre>5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199</pre> ==={{header\|GW-BASIC}}=== {{works with\|BASICA}} <syntaxhighlight lang="gwbasic">10 REM Numbers which binary and ternary digit sum are prime 20 FOR N = 2 TO 199 30 B = 2 40 GOSUB 200: GOSUB 120 50 IF Q = 0 THEN GOTO 90 60 B = 3 70 GOSUB 200: GOSUB 120 80 IF Q = 1 THEN PRINT USING "### ";N; 90 NEXT N 100 PRINT 110 END 120 REM tests if a number is prime 130 IF P = 3 OR P = 2 THEN Q = 1: RETURN 140 IF P = 1 THEN Q = 0: RETURN 150 Q = 1: I = 1 160 I = I + 1 170 IF P MOD I = 0 THEN Q = 0 180 IF I * I <= P AND Q <> 0 THEN GOTO 160 190 RETURN 200 REM finds the digit sum of N in base B, returns P 210 P = 0: XN = N 220 WHILE XN <> 0 230 P = P + XN MOD B 240 XN = XN \ B 250 WEND 260 RETURN</syntaxhighlight> {{out}}<pre> 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199</pre> '''Another solution''' None of the digit sums are higher than 9, so the easiest thing to do is to hardcode which ones are prime. ~~<lang BASIC>10 DEFINT I,J,K,P~~ {{works with\|BASICA}} ~~20 DIM P(9): DATA 0,1,1,0,1,0,1,0,0~~ <syntaxhighlight lang="gwbasic">10 REM Numbers which binary and ternary digit sum are prime ~~30 FOR I=1 TO 9: READ P(I): NEXT~~ 20 DEFINT I,J,K,P ~~40 FOR I=0 TO 199~~ 30 DIM P(9): DATA 0,1,1,0,1,0,1,0,0 ~~50 J=0: K=I~~ 40 FOR I=1 TO 9: READ P(I): NEXT ~~60 IF K>0 THEN J=J+K MOD 2: K=K\2: GOTO 60 ELSE IF P(J)=0 THEN 90~~ 7050 JFOR I=0: ~~K=I~~TO 199 60 J=0: K=I ~~80 IF K>0 THEN J=J+K MOD 3: K=K\3: GOTO 80 ELSE IF P(J) THEN PRINT I,~~ 70 IF K>0 THEN J=J+K MOD 2: K=K\2: GOTO 70 ELSE IF P(J)=0 THEN 100 ~~90 NEXT I</lang>~~ 80 J=0: K=I 90 IF K>0 THEN J=J+K MOD 3: K=K\3: GOTO 90 ELSE IF P(J) THEN PRINT I, 100 NEXT I 110 END</syntaxhighlight> {{out}} <pre> 5 6 7 10 11 Line 253 ⟶ 413: 179 181 185 191 193 199</pre> ==={{header\|Tiny BASIC}}=== This isn't a very interesting problem. The most illustrative part of this solution is that it only uses four variables; several have multiple purposes. Efficiency is important when the language has only 26 variable names in total. <syntaxhighlight lang="tinybasic"> REM B digital base input to sumdig, also output of primality routine REM N input to sumdig routine REM P input to primality routine, output of sumdig routine REM T temp variable in sumdig routine, loop var in prime routine LET N = 1 20 LET N = N + 1 LET B = 2 GOSUB 200 GOSUB 100 IF B = 0 THEN GOTO 30 LET B = 3 GOSUB 200 GOSUB 100 IF B = 1 THEN PRINT N 30 IF N < 200 THEN GOTO 20 END 100 REM PRIMALITY BY TRIAL DIVISION LET B = 0 IF P = 1 THEN RETURN LET B = 1 IF P = 2 THEN RETURN LET T = 2 110 IF (P/T)T = P THEN LET B = 0 IF B = 0 THEN RETURN LET T = T + 1 IF TT <= P THEN GOTO 110 RETURN 200 REM digital sum of N in base B LET T = N LET P = 0 210 IF T = 0 THEN RETURN LET P = P + T - (T/B)B LET T = T/B GOTO 210 </syntaxhighlight> =={{header\|BCPL}}== <~~lang~~syntaxhighlight lang="bcpl">get "libhdr" let digitsum(n, base) = Line 279 ⟶ 481: $) wrch('N') $)</~~lang~~syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 Line 290 ⟶ 492: =={{header\|C}}== <~~lang~~syntaxhighlight lang="c">#include <stdio.h> #include <stdint.h> Line 323 ⟶ 525: printf("\n"); return 0; }</~~lang~~syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 Line 331 ⟶ 533: 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199</pre> =={{header\|CLU}}== <syntaxhighlight lang="clu">prime = proc (n: int) returns (bool) if n<2 then return(false) end for i: int in int$from_to(2, n-1) do if n//i=0 then return(false) end end return(true) end prime digit_sum = proc (n, base: int) returns (int) sum: int := 0 while n>0 do sum := sum + n//base n := n/base end return(sum) end digit_sum start_up = proc () po: stream := stream$primary_output() n: int := 0 for i: int in int$from_to(2, 199) do s2: int := digit_sum(i,2) s3: int := digit_sum(i,3) if prime(s2) cand prime(s3) then stream$putright(po, int$unparse(i), 4) n := n + 1 if n // 20 = 0 then stream$putl(po, "") end end end end start_up</syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199</pre> =={{header\|Cowgol}}== <~~lang~~syntaxhighlight lang="cowgol">include "cowgol.coh"; sub prime(n: uint8): (p: uint8) is Line 365 ⟶ 604: end if; n := n + 1; end loop;</~~lang~~syntaxhighlight> {{out}} <pre style='height:50ex;'>5 Line 428 ⟶ 667: 193 199</pre> =={{header\|Delphi}}== {{works with\|Delphi\|6.0}} {{libheader\|SysUtils,StdCtrls}} <syntaxhighlight lang="Delphi"> function IsPrime(N: int64): boolean; {Fast, optimised prime test} var I,Stop: int64; begin if (N = 2) or (N=3) then Result:=true else if (n <= 1) or ((n mod 2) = 0) or ((n mod 3) = 0) then Result:= false else begin I:=5; Stop:=Trunc(sqrt(N+0.0)); Result:=False; while I<=Stop do begin if ((N mod I) = 0) or ((N mod (I + 2)) = 0) then exit; Inc(I,6); end; Result:=True; end; end; function SumDigitsByBase(N,Base: integer): integer; {Sum all digits of N in the specified B} var I: integer; begin Result:=0; repeat begin I:=N mod Base; Result:=Result+I; N:=N div Base; end until N = 0; end; function IsBinaryTernaryPrime(N: integer): boolean; {Test if sums of binary and ternary digits is prime} var Sum2,Sum3: integer; begin Result:=IsPrime(SumDigitsByBase(N,2)) and IsPrime(SumDigitsByBase(N,3)); end; procedure ShowBinaryTernaryPrimes(Memo: TMemo); {Show the Binary-Ternary sum primes of first 200 values} var I,Cnt: integer; var S: string; begin S:=''; Cnt:=0; for I:=0 to 200-1 do if IsBinaryTernaryPrime(I) then begin Inc(Cnt); S:=S+Format('%8D',[I]); If (Cnt mod 5)=0 then S:=S+CRLF; end; Memo.Lines.Add(S); Memo.Lines.Add('Count= '+IntToStr(Cnt)); end; </syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Count= 61 Elapsed Time: 3.322 ms. </pre> =={{header\|F_Sharp\|F#}}== This task uses [http://www.rosettacode.org/wiki/Extensible_prime_generator#The_functions Extensible Prime Generator (F#)] <~~lang~~syntaxhighlight lang="fsharp"> // binary and ternary digit sums are prime: Nigel Galloway. April 16th., 2021 let fN2,fN3=let rec fG n g=function l when l<n->l+g \|l->fG n (g+l%n)(l/n) in (fG 2 0, fG 3 0) {0..200}\|>Seq.filter(fun n->isPrime(fN2 n) && isPrime(fN3 n))\|>Seq.iter(printf "%d "); printfn "" </syntaxhighlight> ~~</lang>~~ {{out}} <pre> Line 444 ⟶ 771: =={{header\|Factor}}== {{works with\|Factor\|0.99 2021-02-05}} <~~lang~~syntaxhighlight lang="factor">USING: combinators combinators.short-circuit formatting io lists lists.lazy math math.parser math.primes sequences ; Line 463 ⟶ 790: "Base 10 Base 2 (sum) Base 3 (sum)" print l23primes [ 200 < ] lwhile [ 23prime. ] leach</~~lang~~syntaxhighlight> {{out}} <pre style="height:24em"> Line 529 ⟶ 856: 199 11000111 5 21101 5 </pre> =={{header\|Fermat}}== <syntaxhighlight lang="fermat">Function Digsum(n, b) = digsum := 0; while n>0 do digsum := digsum + n\|b; n:=n\b; od; digsum.; for p=1 to 200 do if Isprime(Digsum(p,3)) and Isprime(Digsum(p,2)) then !(p,' '); nadd := nadd+1; fi od;</syntaxhighlight> {{out}}<pre>5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199</pre> =={{header\|FOCAL}}== <~~lang~~syntaxhighlight lang="focal">01.10 S P(2)=1;S P(3)=1;S P(5)=1;S P(7)=1 01.20 S V=10 01.30 F N=0,199;D 3 Line 550 ⟶ 893: 03.50 S V=V-1 03.60 I (-V)3.7;T !;S V=10 03.70 R</~~lang~~syntaxhighlight> {{out}} <pre>= 5= 6= 7= 10= 11= 12= 13= 17= 18= 19 Line 559 ⟶ 902: = 157= 162= 167= 171= 173= 179= 181= 185= 191= 193 = 199</pre> =={{header\|Fōrmulæ}}== {{FormulaeEntry\|page=https://formulae.org/?script=examples/Numbers_which_binary_and_ternary_digit_sum_are_prime}} '''Solution''' [[File:Fōrmulæ - Numbers which binary and ternary digit sum are prime 01.png]] [[File:Fōrmulæ - Numbers which binary and ternary digit sum are prime 02.png]] =={{header\|Go}}== {{trans\|Wren}} {{libheader\|Go-rcu}} <syntaxhighlight lang="go">package main import ( "fmt" "rcu" ) func main() { var numbers []int for i := 2; i < 200; i++ { bds := rcu.DigitSum(i, 2) if rcu.IsPrime(bds) { tds := rcu.DigitSum(i, 3) if rcu.IsPrime(tds) { numbers = append(numbers, i) } } } fmt.Println("Numbers < 200 whose binary and ternary digit sums are prime:") for i, n := range numbers { fmt.Printf("%4d", n) if (i+1)%14 == 0 { fmt.Println() } } fmt.Printf("\n\n%d such numbers found\n", len(numbers)) }</syntaxhighlight> {{out}} <pre> Numbers < 200 whose binary and ternary digit sums are prime: 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 61 such numbers found </pre> =={{header\|Haskell}}== <~~lang~~syntaxhighlight lang="haskell">import Data.Bifunctor (first) import Data.List.Split (chunksOf) import Data.Numbers.Primes (isPrime) Line 600 ⟶ 996: justifyRight :: Int -> Char -> String -> String justifyRight n c = (drop . length) <> (replicate n c <>)</~~lang~~syntaxhighlight> <pre>61 matches in [1..199] Line 612 ⟶ 1,008: =={{header\|J}}== <~~lang~~syntaxhighlight Jlang="j">((1./@p:2 3+/@(#.^:_1)"0])"0#]) i.200</~~lang~~syntaxhighlight> {{out}} <pre>5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199</pre> =={{header\|jq}}== '''Adapted from [[#Wren\|Wren]]''' {{works with\|jq}} '''Also works with gojq, the Go implementation of jq, and with fq''' <syntaxhighlight lang=jq> def lpad($len): tostring \| ($len - length) as $l \| (" " * $l)[:$l] + .; def sum(s): reduce s as $_ (0; . + $_); def is_prime: . as $n \| if ($n < 2) then false elif ($n % 2 == 0) then $n == 2 elif ($n % 3 == 0) then $n == 3 elif ($n % 5 == 0) then $n == 5 elif ($n % 7 == 0) then $n == 7 elif ($n % 11 == 0) then $n == 11 elif ($n % 13 == 0) then $n == 13 elif ($n % 17 == 0) then $n == 17 elif ($n % 19 == 0) then $n == 19 else 23 \| until( (. * .) > $n or ($n % . == 0); .+2) \| . * . > $n end; def digitSum($base): def stream: recurse(if . > 0 then ./$base\|floor else empty end) \| . % $base ; sum(stream); def digit_sums_are_prime($n): [range(2;$n) \| digitSum(2) as $bds \| select($bds\|is_prime) \| digitSum(3) as $tds \| select($tds\|is_prime) ]; def task($n): "Numbers < \($n) whose binary and ternary digit sums are prime:", (digit_sums_are_prime($n) \| length as $length \| (_nwise(14) \| map(lpad(4)) \| join(" ")), "\nFound \($length) such numbers." ); task(200) </syntaxhighlight> {{output}} <pre> Numbers < 200 whose binary and ternary digit sums are prime: 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 Found 61 such numbers. </pre> =={{header\|Julia}}== <~~lang~~syntaxhighlight lang="julia">using Primes btsumsareprime(n) = isprime(sum(digits(n, base=2))) && isprime(sum(digits(n, base=3))) foreach(p -> print(rpad(p[2], 4), p[1] % 20 == 0 ? "\n" : ""), enumerate(filter(btsumsareprime, 1:199))) </~~lang~~syntaxhighlight>{{out}} <pre> 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 Line 631 ⟶ 1,085: =={{header\|MAD}}== <~~lang~~syntaxhighlight lang="mad"> NORMAL MODE IS INTEGER INTERNAL FUNCTION(P) Line 659 ⟶ 1,113: VECTOR VALUES FMT = $I3$ END OF PROGRAM </~~lang~~syntaxhighlight> {{out}} <pre style='height:50ex;'> 5 Line 722 ⟶ 1,176: 193 199</pre> =={{header\|Mathematica}} / {{header\|Wolfram Language}}== <syntaxhighlight lang="mathematica">Partition[ Select[ Range@ 200, (PrimeQ[Total@IntegerDigits[#, 2]] && PrimeQ[Total@IntegerDigits[#, 3]]) &], UpTo[8]] // TableForm</syntaxhighlight> {{out}}<pre> 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 </pre> =={{header\|Nim}}== <~~lang~~syntaxhighlight ~~Nim~~lang="nim">import strutils func isPrime(n: Positive): bool = Line 750 ⟶ 1,221: stdout.write ($n).align(3), if count mod 16 == 0: '\n' else: ' ' echo() echo "Found ", count, " numbers."</~~lang~~syntaxhighlight> {{out}} Line 761 ⟶ 1,232: =={{header\|Perl}}== {{libheader\|ntheory}} <~~lang~~syntaxhighlight lang="perl">use strict; use warnings; use feature 'say'; Line 771 ⟶ 1,242: my @p; test_digits($_,2) and test_digits($_,3) and push @p, $_ for 1..199; say my $result = @p . " matching numbers:\n" . (sprintf "@{['%4d' x @p]}", @p) =~ s/(.{40})/$1\n/gr;</~~lang~~syntaxhighlight> {{out}} <pre>61 matching numbers: Line 781 ⟶ 1,252: 157 162 167 171 173 179 181 185 191 193 199</pre> =={{header\|Phix}}== <!--<syntaxhighlight lang="phix">(phixonline)--> <span style="color: #008080;">function</span> <span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">)</span> <span style="color: #004080;">string</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span> <span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #008080;">end</span> <span style="color: #008080;">while</span> <span style="color: #008080;">return</span> <span style="color: #000000;">result</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #008080;">function</span> <span style="color: #000000;">prime23</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">return</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)))</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)))</span> <span style="color: #008080;">end</span> <span style="color: #008080;">function</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">199</span><span style="color: #0000FF;">),</span><span style="color: #000000;">prime23</span><span style="color: #0000FF;">)</span> <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d numbers found: %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)})</span> <!--</syntaxhighlight>--> {{out}} <pre> 61 numbers found: {5,6,7,10,11,"...",181,185,191,193,199} </pre> =={{Header\|PL/I}}== See [[#Polyglot:PL/I and PL/M]] =={{header\|PL/M}}== <~~lang~~syntaxhighlight ~~plm~~lang="pli">100H: / CP/M CALLS / BDOS: PROCEDURE (FN, ARG); DECLARE FN BYTE, ARG ADDRESS; GO TO 5; END BDOS; Line 831 ⟶ 1,331: CALL EXIT; EOF</~~lang~~syntaxhighlight> {{out}} <pre style='height:50ex;'>5 Line 894 ⟶ 1,394: 193 199</pre> See also [[#Polyglot:PL/I and PL/M]] =={{header\|Plain English}}== <~~lang~~syntaxhighlight lang="plainenglish">To run: Start up. Loop. Line 923 ⟶ 1,425: Find another digit sum of the number given 3. If the other digit sum is not prime, say no. Say yes.</~~lang~~syntaxhighlight> {{out}} <pre> Line 929 ⟶ 1,431: </pre> =={{header\|~~Phix~~Polyglot:PL/I and PL/M}}== {{works with\|8080 PL/M Compiler}} ... under CP/M (or an emulator) ~~<!--<lang Phix>(phixonline)-->~~ Should work with many PL/I implementations. <span style="color: #008080;">function</span> <span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">base</span><span style="color: #0000FF;">)</span> <br> ~~<span style="color: #004080;">string</span> <span style="color: #000000;">result</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>~~ The PL/I include file "pg.inc" can be found on the [[Polyglot:PL/I and PL/M]] page. ~~<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>~~ Note the use of text in column 81 onwards to hide the PL/I specifics from the PL/M compiler. <span style="color: #000000;">result</span> <span style="color: #0000FF;">&=</span> <span style="color: #7060A8;">remainder</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span> <syntaxhighlight lang="pli">/ FIND NUMBERS WHOSE DIGIT SUM SQUARED AND CUBED IS PRIME / <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">/</span><span style="color: #000000;">base</span><span style="color: #0000FF;">)</span> prime_digit_sums_100H: procedure options (main); <span style="color: #008080;">if</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> ~~<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>~~ / PL/I DEFINITIONS / ~~<span style="color: #008080;">return</span> <span style="color: #000000;">result</span>~~ %include 'pg.inc'; ~~<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>~~ / PL/M DEFINITIONS: CP/M BDOS SYSTEM CALL AND CONSOLE I/O ROUTINES, ETC. / / DECLARE BINARY LITERALLY 'ADDRESS', CHARACTER LITERALLY 'BYTE'; <span style="color: #008080;">function</span> <span style="color: #000000;">prime23</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> DECLARE FIXED LITERALLY ' ', BIT LITERALLY 'BYTE'; <span style="color: #008080;">return</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)))</span> DECLARE STATIC LITERALLY ' ', RETURNS LITERALLY ' '; <span style="color: #008080;">and</span> <span style="color: #7060A8;">is_prime</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">to_base</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">)))</span> DECLARE FALSE LITERALLY '0', TRUE LITERALLY '1'; ~~<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>~~ DECLARE HBOUND LITERALLY 'LAST', SADDR LITERALLY '.'; BDOSF: PROCEDURE( FN, ARG )BYTE; <span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">filter</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">199</span><span style="color: #0000FF;">),</span><span style="color: #000000;">prime23</span><span style="color: #0000FF;">)</span> DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END; <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%d numbers found: %V\n"</span><span style="color: #0000FF;">,{</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">shorten</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)})</span> BDOS: PROCEDURE( FN, ARG ); DECLARE FN BYTE, ARG ADDRESS; GOTO 5; END; ~~<!--</lang>-->~~ PRCHAR: PROCEDURE( C ); DECLARE C BYTE; CALL BDOS( 2, C ); END; PRSTRING: PROCEDURE( S ); DECLARE S ADDRESS; CALL BDOS( 9, S ); END; PRNL: PROCEDURE; CALL PRCHAR( 0DH ); CALL PRCHAR( 0AH ); END; PRNUMBER: PROCEDURE( N ); DECLARE N ADDRESS; DECLARE V ADDRESS, N$STR( 6 ) BYTE, W BYTE; N$STR( W := LAST( N$STR ) ) = '$'; N$STR( W := W - 1 ) = '0' + ( ( V := N ) MOD 10 ); DO WHILE( ( V := V / 10 ) > 0 ); N$STR( W := W - 1 ) = '0' + ( V MOD 10 ); END; CALL BDOS( 9, .N$STR( W ) ); END PRNUMBER; MODF: PROCEDURE( A, B )ADDRESS; DECLARE ( A, B )ADDRESS; RETURN( A MOD B ); END MODF; /* END LANGUAGE DEFINITIONS / / TASK / DIGITSUM: PROCEDURE( N, BASE )RETURNS / RETURNS THE DIGIT SUM OF N / ( FIXED BINARY / IN THE SPECIFIED BASE / ) ; DECLARE ( N, BASE ) FIXED BINARY; DECLARE ( SUM, V ) FIXED BINARY; SUM = MODF( N, BASE ); V = N / BASE; DO WHILE( V > 0 ); SUM = SUM + MODF( V, BASE ); V = V / BASE; END; RETURN( SUM ); END DIGITSUM ; ISPRIME: PROCEDURE( N )RETURNS / RETURNS TRUE IF N IS PRIME, / ( BIT / FALSE OTHERWISE / ) ; DECLARE N FIXED BINARY; DECLARE I FIXED BINARY; DECLARE RESULT BIT; IF N < 2 THEN RESULT = FALSE; ELSE IF N = 2 THEN RESULT = TRUE; ELSE IF MODF( N, 2 ) = 0 THEN RESULT = FALSE; ELSE DO; RESULT = TRUE; I = 3; DO WHILE( RESULT & / AND /* / ( I I ) <= N ); RESULT = MODF( N, I ) > 0; I = I + 2; END; END; RETURN( RESULT ); END ISPRIME ; DECLARE ( I, PCOUNT ) FIXED BINARY; PCOUNT = 0; DO I = 1 TO 199; IF ISPRIME( DIGITSUM( I, 2 ) ) THEN DO; IF ISPRIME( DIGITSUM( I, 3 ) ) THEN DO; CALL PRCHAR( ' ' ); IF I < 10 THEN CALL PRCHAR( ' ' ); IF I < 100 THEN CALL PRCHAR( ' ' ); CALL PRNUMBER( I ); PCOUNT = PCOUNT + 1; IF PCOUNT > 9 THEN DO; PCOUNT = 0; CALL PRNL; END; END; END; END; EOF: end prime_digit_sums_100H;</syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 ~~61 numbers found: {5,6,7,10,11,"...",181,185,191,193,199}~~ 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 </pre> =={{header\|Python}}== <~~lang~~syntaxhighlight lang="python">'''Binary and Ternary digit sums both prime''' Line 1,044 ⟶ 1,628: if __name__ == '__main__': main() </syntaxhighlight> ~~</lang>~~ <pre>61 matches in [1..199] Line 1,054 ⟶ 1,638: 157 162 167 171 173 179 181 185 191 193 199</pre> =={{header\|Quackery}}== <code>digitsum</code> is defined at [[Sum digits of an integer#Quackery]]. <code>isprime</code> is defined at [[Primality by trial division#Quackery]]. <syntaxhighlight lang="Quackery"> [] 200 times [ i^ 3 digitsum isprime while i^ 2 digitsum isprime while i^ join ] echo</syntaxhighlight> {{out}} <pre>[ 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 ]</pre> =={{header\|Raku}}== <syntaxhighlight lang="raku" ~~perl6~~line>say (^200).grep(-> $n {all (2,3).map({$n.base($_).comb.sum.is-prime}) }).batch(10)».fmt('%3d').join: "\n";</~~lang~~syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 Line 1,068 ⟶ 1,669: =={{header\|REXX}}== <~~lang~~syntaxhighlight lang="rexx">/REXX program finds and displays integers whose base 2 and base 3 digit sums are prime./ parse arg n cols . /obtain optional argument from the CL./ if n=='' \| n=="," then n= 200 /Not specified? Then use the default./ Line 1,080 ⟶ 1,681: $= /a list of numbers found (so far). / do j=1 for n-1 /find #s whose B2 & B3 sums are prime./ b2= sumDig( tBase(j, 2) ); if \!.b2 then iterate /convert to base2, sum digits./ /* ◄■■■■■■■■ a filter. / b3= sumDig( tBase(j, 3) ); if \!.b3 then iterate / " " base3 " " / / ◄■■■■■■■■ a filter. / found= found + 1 /bump the number of found integers. / if cols<1 then iterate /Only showing the summary? Then skip./ Line 1,105 ⟶ 1,706: do while x>=toBase; y= substr($, x//toBase+1, 1)y; x= x % toBase end /while*/ return substr($, x+1, 1)y</~~lang~~syntaxhighlight> {{out\|output\|text=  when using the default inputs:}} <pre> Line 1,123 ⟶ 1,724: =={{header\|Ring}}== <~~lang~~syntaxhighlight lang="ring"> load "stdlib.ring" Line 1,170 ⟶ 1,771: binList = substr(binList,nl,"") return binList </syntaxhighlight> ~~</lang>~~ {{out}} <pre style="height:24em"> Line 1,238 ⟶ 1,839: Found 61 such numbers done... </pre> =={{header\|Ruby}}== <syntaxhighlight lang="ruby"> require 'prime' p (1..200).select{\|n\| [2, 3].all?{\|base\| n.digits(base).sum.prime?} }</syntaxhighlight> {{out}} <pre> [5, 6, 7, 10, 11, 12, 13, 17, 18, 19, 21, 25, 28, 31, 33, 35, 36, 37, 41, 47, 49, 55, 59, 61, 65, 67, 69, 73, 79, 82, 84, 87, 91, 93, 97, 103, 107, 109, 115, 117, 121, 127, 129, 131, 133, 137, 143, 145, 151, 155, 157, 162, 167, 171, 173, 179, 181, 185, 191, 193, 199] </pre> =={{header\|Sidef}}== <syntaxhighlight lang="ruby">1..^200 -> grep {\|n\| [2,3].all { n.sumdigits(_).is_prime } }</syntaxhighlight> {{out}} <pre> [5, 6, 7, 10, 11, 12, 13, 17, 18, 19, 21, 25, 28, 31, 33, 35, 36, 37, 41, 47, 49, 55, 59, 61, 65, 67, 69, 73, 79, 82, 84, 87, 91, 93, 97, 103, 107, 109, 115, 117, 121, 127, 129, 131, 133, 137, 143, 145, 151, 155, 157, 162, 167, 171, 173, 179, 181, 185, 191, 193, 199] </pre> Line 1,243 ⟶ 1,861: {{libheader\|Wren-math}} {{libheader\|Wren-fmt}} <syntaxhighlight lang="wren">import "./math" for Int ~~{{libheader\|Wren-seq}}~~ ~~<lang ecmascript>~~import "./~~math~~fmt" for ~~Int~~Fmt ~~import "/fmt" for Fmt~~ ~~import "/seq" for Lst~~ var numbers = [] Line 1,257 ⟶ 1,873: } System.print("Numbers < 200 whose binary and ternary digit sums are prime:") Fmt.tprint("$4d", numbers, 14) ~~for (chunk in Lst.chunks(numbers, 14)) Fmt.print("$4d", chunk)~~ System.print("\nFound %(numbers.count) such numbers.")</~~lang~~syntaxhighlight> {{out}} Line 1,270 ⟶ 1,886: Found 61 such numbers. </pre> =={{header\|XPL0}}== <syntaxhighlight lang="xpl0">func IsPrime(N); \Return 'true' if N is a prime number int N, I; [if N <= 1 then return false; for I:= 2 to sqrt(N) do if rem(N/I) = 0 then return false; return true; ]; func SumDigits(N, Base); \Return sum of digits in N for Base int N, Base, Sum; [Sum:= 0; repeat N:= N/Base; Sum:= Sum + rem(0); until N=0; return Sum; ]; int Count, N; [Count:= 0; for N:= 0 to 200-1 do if IsPrime(SumDigits(N,2)) & IsPrime(SumDigits(N,3)) then [IntOut(0, N); Count:= Count+1; if rem(Count/10) = 0 then CrLf(0) else ChOut(0, 9\tab\); ]; CrLf(0); IntOut(0, Count); Text(0, " such numbers found below 200. "); ]</syntaxhighlight> {{out}} <pre> 5 6 7 10 11 12 13 17 18 19 21 25 28 31 33 35 36 37 41 47 49 55 59 61 65 67 69 73 79 82 84 87 91 93 97 103 107 109 115 117 121 127 129 131 133 137 143 145 151 155 157 162 167 171 173 179 181 185 191 193 199 61 such numbers found below 200. </pre>