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Numbers which binary and ternary digit sum are prime

From Rosetta Code
Numbers which binary and ternary digit sum are prime is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.
Task
Show numbers which binary and ternary digit sum are prime, where n < 200




ALGOL 68[edit]

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;
OP DIGITSUM = ( INT n, b )INT:
BEGIN
INT d sum := 0;
INT v := ABS n;
WHILE v > 0 DO
d sum +:= v MOD b;
v OVERAB b
OD;
d sum
END # DIGITSUM # ;
INT max number = 200;
[]BOOL prime = sieve( max number );
INT n count := 0;
FOR n TO max number DO
INT d sum 2 = n DIGITSUM 2;
IF prime[ d sum 2 ] THEN
INT d sum 3 = n DIGITSUM 3;
IF prime[ d sum 3 ] THEN
# the base 2 and base 3 digit sums of n are both prime #
print( ( " ", whole( n, -3 ), IF prime[ n ] THEN "*" ELSE " " FI ) );
n count +:= 1;
IF n count MOD 14 = 0 THEN print( ( newline ) ) FI
FI
FI
OD;
print( ( newline ) );
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
Output:
   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 whose binary and ternary digit sums are prime
    those that are themselves prime are suffixed with a "*"

Factor[edit]

Works with: Factor version 0.99 2021-02-05
USING: combinators combinators.short-circuit formatting io lists
lists.lazy math math.parser math.primes sequences ;
 
: dsum ( n base -- sum ) >base [ digit> ] map-sum ;
: dprime? ( n base -- ? ) dsum prime? ;
: 23prime? ( n -- ? ) { [ 2 dprime? ] [ 3 dprime? ] } 1&& ;
: l23primes ( -- list ) 1 lfrom [ 23prime? ] lfilter ;
 
: 23prime. ( n -- )
{
[ ]
[ >bin ]
[ 2 dsum ]
[ 3 >base ]
[ 3 dsum ]
} cleave
"%-8d %-9s %-6d %-7s %d\n" printf ;
 
"Base 10 Base 2 (sum) Base 3 (sum)" print
l23primes [ 200 < ] lwhile [ 23prime. ] leach
Output:
Base 10  Base 2    (sum)  Base 3  (sum)
5        101       2      12      3
6        110       2      20      2
7        111       3      21      3
10       1010      2      101     2
11       1011      3      102     3
12       1100      2      110     2
13       1101      3      111     3
17       10001     2      122     5
18       10010     2      200     2
19       10011     3      201     3
21       10101     3      210     3
25       11001     3      221     5
28       11100     3      1001    2
31       11111     5      1011    3
33       100001    2      1020    3
35       100011    3      1022    5
36       100100    2      1100    2
37       100101    3      1101    3
41       101001    3      1112    5
47       101111    5      1202    5
49       110001    3      1211    5
55       110111    5      2001    3
59       111011    5      2012    5
61       111101    5      2021    5
65       1000001   2      2102    5
67       1000011   3      2111    5
69       1000101   3      2120    5
73       1001001   3      2201    5
79       1001111   5      2221    7
82       1010010   3      10001   2
84       1010100   3      10010   2
87       1010111   5      10020   3
91       1011011   5      10101   3
93       1011101   5      10110   3
97       1100001   3      10121   5
103      1100111   5      10211   5
107      1101011   5      10222   7
109      1101101   5      11001   3
115      1110011   5      11021   5
117      1110101   5      11100   3
121      1111001   5      11111   5
127      1111111   7      11201   5
129      10000001  2      11210   5
131      10000011  3      11212   7
133      10000101  3      11221   7
137      10001001  3      12002   5
143      10001111  5      12022   7
145      10010001  3      12101   5
151      10010111  5      12121   7
155      10011011  5      12202   7
157      10011101  5      12211   7
162      10100010  3      20000   2
167      10100111  5      20012   5
171      10101011  5      20100   3
173      10101101  5      20102   5
179      10110011  5      20122   7
181      10110101  5      20201   5
185      10111001  5      20212   7
191      10111111  7      21002   5
193      11000001  3      21011   5
199      11000111  5      21101   5

Julia[edit]

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)))
 
Output:
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

Phix[edit]

function to_base(atom n, integer base)
    string result = ""
    while true do
        result &= remainder(n,base)
        n = floor(n/base)
        if n=0 then exit end if
    end while
    return result
end function

function prime23(integer n)
    return is_prime(sum(to_base(n,2)))
       and is_prime(sum(to_base(n,3)))
end function

sequence res = filter(tagset(199),prime23)
printf(1,"%d numbers found: %V\n",{length(res),shorten(res,"",5)})
Output:
61 numbers found: {5,6,7,10,11,"...",181,185,191,193,199}

Raku[edit]

say (^200).grep(-> $n {all (2,3).map({$n.base($_).comb.sum.is-prime}) }).batch(10)».fmt('%3d').join: "\n";
Output:
  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

REXX[edit]

/*REXX program finds and displays integers whose base 2 and base 3 digit sums are prime.*/
parse arg hi cols . /*obtain optional argument from the CL.*/
if hi=='' | hi=="," then hi= 200 /*Not specified? Then use the default.*/
if cols=='' | cols=="," then cols= 10 /* " " " " " " */
call genP /*build array of semaphores for primes.*/
w= 10 /*width of a number in any column. */
@b2b3= ' numbers < ' commas(hi) " whose binary and ternary digit sums are prime"
if cols>0 then say ' index │'center(@b2b3, 1 + cols*(w+1) )
if cols>0 then say '───────┼'center("" , 1 + cols*(w+1), '─')
finds= 0; idx= 1 /*initialize # of finds and the index. */
$= /*a list of numbers found (so far). */
do j=1 to hi-1 /*find #s whose B2 & B3 sums are prime.*/
b2= sumDig( tBase(j, 2) ); if \!.b2 then iterate /*convert to base2, sum digits*/
b3= sumDig( tBase(j, 3) ); if \!.b3 then iterate /* " " base3 " " */
finds= finds + 1 /*bump the number of found integers. */
if cols==0 then iterate /*Build the list (to be shown later)? */
c= commas(j) /*maybe add commas to the number. */
$= $ right(c, max(w, length(c) ) ) /*add an integer ──► $ list, allow big#*/
if finds//cols\==0 then iterate /*have we populated a line of output? */
say center(idx, 7)'│' substr($, 2); $= /*display what we have so far (cols). */
idx= idx + cols /*bump the index count for the output*/
end /*j*/
 
if $\=='' then say center(idx, 7)"│" substr($, 2) /*possible display residual output.*/
say
say 'Found ' commas(finds) @b2b3
exit 0 /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
commas: parse arg ?; do jc=length(?)-3 to 1 by -3; ?=insert(',', ?, jc); end; return ?
sumDig: procedure; parse arg x 1 s 2;do j=2 for length(x)-1;s=s+substr(x,j,1);end;return s
/*──────────────────────────────────────────────────────────────────────────────────────*/
genP:  !.=0; @= '2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97'
#= words(@); do p=1 for #; _= word(@, p);  !._= 1; end; return
/*──────────────────────────────────────────────────────────────────────────────────────*/
tBase: procedure; parse arg x,toBase; y=; $= 0123456789
do while x>=toBase; y= substr($, x//toBase+1, 1)y; x= x%toBase
end /*while*/
return substr($, x+1, 1)y
output   when using the default inputs:
 index │                         numbers  <  200  whose binary and ternary digit sums are prime
───────┼───────────────────────────────────────────────────────────────────────────────────────────────────────────────
   1   │          5          6          7         10         11         12         13         17         18         19
  11   │         21         25         28         31         33         35         36         37         41         47
  21   │         49         55         59         61         65         67         69         73         79         82
  31   │         84         87         91         93         97        103        107        109        115        117
  41   │        121        127        129        131        133        137        143        145        151        155
  51   │        157        162        167        171        173        179        181        185        191        193
  61   │        199

Found  61  numbers  <  200  whose binary and ternary digit sums are prime

Ring[edit]

 
load "stdlib.ring"
 
see "working..." + nl
see "Numbers < 200 whose binary and ternary digit sums are prime:" + nl
 
decList = [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]
baseList = ["0","1","2","3","4","5","6","7","8","9","A","B","C","D","E","F"]
 
num = 0
limit = 200
 
for n = 1 to limit
strBin = decimaltobase(n,2)
strTer = decimaltobase(n,3)
sumBin = 0
for m = 1 to len(strBin)
sumBin = sumBin + number(strBin[m])
next
sumTer = 0
for m = 1 to len(strTer)
sumTer = sumTer + number(strTer[m])
next
if isprime(sumBin) and isprime(sumTer)
num = num + 1
see "" + num + ". {" + n + "," + strBin + ":" + sumBin + "," + strTer + ":" + sumTer + "}" + nl
ok
next
 
see "Found " + num + " such numbers" + nl
see "done..." + nl
 
func decimaltobase(nr,base)
binList = []
binary = 0
remainder = 1
while(nr != 0)
remainder = nr % base
ind = find(decList,remainder)
rem = baseList[ind]
add(binList,rem)
nr = floor(nr/base)
end
binlist = reverse(binList)
binList = list2str(binList)
binList = substr(binList,nl,"")
return binList
 
Output:
working...
Numbers < 200 whose binary and ternary digit sums are prime:
1. {5,101:2,12:3}
2. {6,110:2,20:2}
3. {7,111:3,21:3}
4. {10,1010:2,101:2}
5. {11,1011:3,102:3}
6. {12,1100:2,110:2}
7. {13,1101:3,111:3}
8. {17,10001:2,122:5}
9. {18,10010:2,200:2}
10. {19,10011:3,201:3}
11. {21,10101:3,210:3}
12. {25,11001:3,221:5}
13. {28,11100:3,1001:2}
14. {31,11111:5,1011:3}
15. {33,100001:2,1020:3}
16. {35,100011:3,1022:5}
17. {36,100100:2,1100:2}
18. {37,100101:3,1101:3}
19. {41,101001:3,1112:5}
20. {47,101111:5,1202:5}
21. {49,110001:3,1211:5}
22. {55,110111:5,2001:3}
23. {59,111011:5,2012:5}
24. {61,111101:5,2021:5}
25. {65,1000001:2,2102:5}
26. {67,1000011:3,2111:5}
27. {69,1000101:3,2120:5}
28. {73,1001001:3,2201:5}
29. {79,1001111:5,2221:7}
30. {82,1010010:3,10001:2}
31. {84,1010100:3,10010:2}
32. {87,1010111:5,10020:3}
33. {91,1011011:5,10101:3}
34. {93,1011101:5,10110:3}
35. {97,1100001:3,10121:5}
36. {103,1100111:5,10211:5}
37. {107,1101011:5,10222:7}
38. {109,1101101:5,11001:3}
39. {115,1110011:5,11021:5}
40. {117,1110101:5,11100:3}
41. {121,1111001:5,11111:5}
42. {127,1111111:7,11201:5}
43. {129,10000001:2,11210:5}
44. {131,10000011:3,11212:7}
45. {133,10000101:3,11221:7}
46. {137,10001001:3,12002:5}
47. {143,10001111:5,12022:7}
48. {145,10010001:3,12101:5}
49. {151,10010111:5,12121:7}
50. {155,10011011:5,12202:7}
51. {157,10011101:5,12211:7}
52. {162,10100010:3,20000:2}
53. {167,10100111:5,20012:5}
54. {171,10101011:5,20100:3}
55. {173,10101101:5,20102:5}
56. {179,10110011:5,20122:7}
57. {181,10110101:5,20201:5}
58. {185,10111001:5,20212:7}
59. {191,10111111:7,21002:5}
60. {193,11000001:3,21011:5}
61. {199,11000111:5,21101:5}
Found 61 such numbers
done...

Wren[edit]

Library: Wren-math
Library: Wren-fmt
Library: Wren-seq
import "/math" for Int
import "/fmt" for Fmt
import "/seq" for Lst
 
var numbers = []
for (i in 2..199) {
var bds = Int.digitSum(i, 2)
if (Int.isPrime(bds)) {
var tds = Int.digitSum(i, 3)
if (Int.isPrime(tds)) numbers.add(i)
}
}
System.print("Numbers < 200 whose binary and ternary digit sums are prime:")
for (chunk in Lst.chunks(numbers, 14)) Fmt.print("$4d", chunk)
System.print("\nFound %(numbers.count) such numbers.")
Output:
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.