Harmonic series: Difference between revisions
Add bruijn
(J draft) |
(Add bruijn) |
||
| (22 intermediate revisions by 13 users not shown) | |||
Line 189:
=={{header|BASIC}}==
==={{header|Applesoft BASIC}}===
The [[#MSX_BASIC|MSX BASIC]] solution works without any changes.
==={{header|BASIC256}}===
<syntaxhighlight lang="freebasic">h = 0.0
Line 208 ⟶ 210:
next i
end</syntaxhighlight>
==={{header|Chipmunk Basic}}===
{{works with|Chipmunk Basic|3.6.4}}
{{works with|GW-BASIC}}
{{works with|QBasic|1.1}}
{{trans|FreeBASIC}}
<syntaxhighlight lang="qbasic">100 cls
110 print "The first twenty harmonic numbers are:"
120 for n = 1 to 20
130 h = h+(1/n)
140 print n,h
150 next n
160 print
170 h = 1
180 n = 2
190 for i = 2 to 10
200 while h < i
210 h = h+(1/n)
220 n = n+1
230 wend
240 print "The first harmonic number greater than ";i;"is ";h;" at position ";n-1
250 next i
260 end</syntaxhighlight>
==={{header|Craft Basic}}===
<syntaxhighlight lang="basic">precision 5
print "the first twenty harmonic numbers are:"
for n = 1 to 20
let h = h + 1 / n
print n, tab, h
next n
print newline, "the nth index of the first harmonic number that exceeds the nth integer:"
let h = 1
let n = 2
for i = 2 to 10
do
if h < i then
let h = h + 1 / n
let n = n + 1
endif
wait
loop h < i
print tab, n - 1,
next i</syntaxhighlight>
{{out| Output}}<pre>
the first twenty harmonic numbers are:
1 1
2 1.50000
3 1.83333
4 2.08333
5 2.28333
6 2.45000
7 2.59286
8 2.71786
9 2.82897
10 2.92897
11 3.01988
12 3.10321
13 3.18013
14 3.25156
15 3.31823
16 3.38073
17 3.43955
18 3.49511
19 3.54774
20 3.59774
The nth index of the first harmonic number that exceeds the nth integer:
4 11 31 83 227 616 1674 4550 12375
</pre>
==={{header|Gambas}}===
{{trans|FreeBASIC}}
<syntaxhighlight lang="vbnet">Public Sub Main()
Dim h As Float = 0
Dim n As Integer, i As Integer
Print "The first twenty harmonic numbers are:"
For n = 1 To 20
h += 1 / n
Print n, h
Next
Print
h = 1
n = 2
For i = 2 To 10
While h < i
h += 1 / n
n += 1
Wend
Print "The first harmonic number greater than "; i; " is "; h; ", at position "; n - 1
Next
End </syntaxhighlight>
{{out}}
<pre>Same as FreeBASIC entry.</pre>
==={{header|GW-BASIC}}===
The [[#MSX_BASIC|MSX BASIC]] solution works without any changes.
==={{header|MSX Basic}}===
{{works with|Applesoft BASIC}}
{{works with|Chipmunk Basic}}
{{works with|PC-BASIC|any}}
{{works with|QBasic}}
<syntaxhighlight lang="qbasic">100 CLS : REM HOME 100 HOME for Applesoft BASIC
110 PRINT "The first twenty harmonic numbers are:"
120 FOR n = 1 TO 20
130 h = h+(1/n)
140 PRINT n,h
150 NEXT n
160 PRINT
170 h = 1
180 n = 2
190 FOR i = 2 TO 10
200 IF NOT(h < i) THEN GOTO 240
210 h = h+(1/n)
220 n = n+1
230 GOTO 200
240 PRINT "The first harmonic number greater than " i "is " h "at position " n-1
250 NEXT i
260 END</syntaxhighlight>
==={{header|QBasic}}===
Line 230 ⟶ 371:
NEXT i
END</syntaxhighlight>
==={{header|Run BASIC}}===
{{works with|Just BASIC}}
{{works with|Liberty BASIC}}
<syntaxhighlight lang="vb">print "The first twenty harmonic numbers are:"
for n = 1 to 20
h = h + 1 / n
print n; chr$(9);h ' print n,h for Just BASIC and Liberty BASIC
next n
print
h = 1
n = 2
for i = 2 to 10
while h < i
h = h + 1 / n
n = n +1
wend
print "The first harmonic number greater than ";i; " is ";h;" at position ";n-1
next i
end</syntaxhighlight>
==={{header|True BASIC}}===
Line 272 ⟶ 433:
end</syntaxhighlight>
=={{header|Bruijn}}==
<syntaxhighlight lang="bruijn">
:import std/List .
:import std/Combinator .
:import std/Math/Rational Q
:import std/Number N
# fun Church iteration hack
harmonic [0 &[[(Q.add 1 op) : N.++0]] start [[1]]] ⧗ Unary → Rational
op (+1) : N.--0
start (+0.0f) : (+1)
custom-gt? &[[[N.gt? 2 (N.mul 0 N.++1)]]] ⧗ Rational → Νumber → Boolean
main [φ cons first-20 first-10-above (harmonic <$> (iterate [[[1 (2 1 0)]]] (+0u)))]
first-20 take (+20)
first-10-above [take (+10) first-above]
first-above [find-index [custom-gt? 0 1] 1] <$> (iterate N.inc (+0))
</syntaxhighlight>
Takes a *long* time, but will return the correct result.
=={{header|C#}}==
{{trans|Go}}
<syntaxhighlight lang="C#">
using System;
using System.Numerics;
public class BigRational
{
public BigInteger Numerator { get; private set; }
public BigInteger Denominator { get; private set; }
public BigRational(BigInteger numerator, BigInteger denominator)
{
if (denominator == 0)
throw new ArgumentException("Denominator cannot be zero.", nameof(denominator));
BigInteger gcd = BigInteger.GreatestCommonDivisor(numerator, denominator);
Numerator = numerator / gcd;
Denominator = denominator / gcd;
if (Denominator < 0)
{
Numerator = -Numerator;
Denominator = -Denominator;
}
}
public static BigRational operator +(BigRational a, BigRational b)
{
return new BigRational(a.Numerator * b.Denominator + b.Numerator * a.Denominator, a.Denominator * b.Denominator);
}
public override string ToString()
{
return $"{Numerator}/{Denominator}";
}
}
class Program
{
static BigRational Harmonic(int n)
{
BigRational sum = new BigRational(0, 1);
for (int i = 1; i <= n; i++)
{
BigRational r = new BigRational(1, i);
sum += r;
}
return sum;
}
static void Main(string[] args)
{
Console.WriteLine("The first 20 harmonic numbers and the 100th, expressed in rational form, are:");
int[] numbers = new int[21];
for (int i = 1; i <= 20; i++)
{
numbers[i - 1] = i;
}
numbers[20] = 100;
foreach (int i in numbers)
{
Console.WriteLine($"{i,3} : {Harmonic(i)}");
}
Console.WriteLine("\nThe first harmonic number to exceed the following integers is:");
const int limit = 10;
for (int i = 1, n = 1; i <= limit; n++)
{
double h = 0;
for (int j = 1; j <= n; j++)
{
h += 1.0 / j;
}
if (h > i)
{
Console.WriteLine($"integer = {i,2} -> n = {n,6} -> harmonic number = {h,9:F6} (to 6dp)");
i++;
}
}
}
}
</syntaxhighlight>
{{out}}
<pre>
The first 20 harmonic numbers and the 100th, expressed in rational form, are:
1 : 1/1
2 : 3/2
3 : 11/6
4 : 25/12
5 : 137/60
6 : 49/20
7 : 363/140
8 : 761/280
9 : 7129/2520
10 : 7381/2520
11 : 83711/27720
12 : 86021/27720
13 : 1145993/360360
14 : 1171733/360360
15 : 1195757/360360
16 : 2436559/720720
17 : 42142223/12252240
18 : 14274301/4084080
19 : 275295799/77597520
20 : 55835135/15519504
100 : 14466636279520351160221518043104131447711/2788815009188499086581352357412492142272
The first harmonic number to exceed the following integers is:
integer = 1 -> n = 2 -> harmonic number = 1.500000 (to 6dp)
integer = 2 -> n = 4 -> harmonic number = 2.083333 (to 6dp)
integer = 3 -> n = 11 -> harmonic number = 3.019877 (to 6dp)
integer = 4 -> n = 31 -> harmonic number = 4.027245 (to 6dp)
integer = 5 -> n = 83 -> harmonic number = 5.002068 (to 6dp)
integer = 6 -> n = 227 -> harmonic number = 6.004367 (to 6dp)
integer = 7 -> n = 616 -> harmonic number = 7.001274 (to 6dp)
integer = 8 -> n = 1674 -> harmonic number = 8.000486 (to 6dp)
integer = 9 -> n = 4550 -> harmonic number = 9.000208 (to 6dp)
integer = 10 -> n = 12367 -> harmonic number = 10.000043 (to 6dp)
</pre>
=={{header|C++}}==
Line 430 ⟶ 734:
4550 9.000208060802
12367 10.000043002313</pre>
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
<syntaxhighlight lang="Delphi">
function HarmonicNumber(N: integer): double;
{Calculate sum of }
var I: integer;
begin
Result:=0;
for I:=1 to N do Result:=Result+1/I;
end;
function FirstHarmonicOver(Limit: integer): integer;
{Find first harmonic number over limit}
var HN: double;
begin
for Result:=1 to high(Integer) do
begin
HN:=HarmonicNumber(Result);
if HN>Limit then exit;
end
end;
procedure ShowHarmonicNumbers(Memo: TMemo);
var I,Inx: integer;
var HN: double;
begin
{Show first 20 harmonic numbers}
for I:=1 to 20 do
begin
HN:=HarmonicNumber(I);
Memo.Lines.Add(Format('%2D: %8.8f',[I,HN]));
end;
{Show the position of the number that exceeds 1..10 }
for I:=1 to 10 do
begin
Inx:=FirstHarmonicOver(I);
Memo.Lines.Add(Format('Position of the first harmonic number > %2D: %4D',[I,Inx]))
end;
end;
</syntaxhighlight>
{{out}}
<pre>
1: 1.00000000
2: 1.50000000
3: 1.83333333
4: 2.08333333
5: 2.28333333
6: 2.45000000
7: 2.59285714
8: 2.71785714
9: 2.82896825
10: 2.92896825
11: 3.01987734
12: 3.10321068
13: 3.18013376
14: 3.25156233
15: 3.31822899
16: 3.38072899
17: 3.43955252
18: 3.49510808
19: 3.54773966
20: 3.59773966
Position of the first harmonic number > 1: 2
Position of the first harmonic number > 2: 4
Position of the first harmonic number > 3: 11
Position of the first harmonic number > 4: 31
Position of the first harmonic number > 5: 83
Position of the first harmonic number > 6: 227
Position of the first harmonic number > 7: 616
Position of the first harmonic number > 8: 1674
Position of the first harmonic number > 9: 4550
Position of the first harmonic number > 10: 12367
</pre>
=={{header|EasyLang}}==
{{trans|BASIC256}}
<syntaxhighlight>
numfmt 5 2
print "The first twenty harmonic numbers are:"
for n = 1 to 20
h += 1 / n
print n & " " & h
.
print ""
print "The first harmonic number greater than: "
h = 1
n = 2
for i = 2 to 10
while h < i
h += 1 / n
n += 1
.
print i & " is " & h & ", at position " & n - 1
.
</syntaxhighlight>
{{out}}
<pre>
The first twenty harmonic numbers are:
1 1
2 1.50000
3 1.83333
4 2.08333
5 2.28333
6 2.45000
7 2.59286
8 2.71786
9 2.82897
10 2.92897
11 3.01988
12 3.10321
13 3.18013
14 3.25156
15 3.31823
16 3.38073
17 3.43955
18 3.49511
19 3.54774
20 3.59774
The first harmonic number greater than:
2 is 2.08333, at position 4
3 is 3.01988, at position 11
4 is 4.02725, at position 31
5 is 5.00207, at position 83
6 is 6.00437, at position 227
7 is 7.00127, at position 616
8 is 8.00049, at position 1674
9 is 9.00021, at position 4550
10 is 10.00004, at position 12367
</pre>
=={{header|Factor}}==
Line 596 ⟶ 1,040:
The first harmonic number greater than 9 is 9.000208062931115, at position 4550
The first harmonic number greater than 10 is 10.00004300827578, at position 12367</pre>
=={{header|FutureBasic}}==
<syntaxhighlight lang="futurebasic">
include "NSLog.incl"
void local fn BuildHamonics
double h = 0.0
long i, n
NSLog( @"The first twenty harmonic numbers are:\n" )
for i = 1 to 20
h = h + 1.0 / i
NSLog( @"%3d. %.8f", i, h )
next
NSLog( @"\n" )
h = 1 : n = 2
for i = 2 to 10
while h < i
h = h + 1.0 / n
n = n + 1
wend
NSLog( @"The first harmonic number > %2d is %11.8f at position %d.", i, h, n -1 )
next
end fn
fn BuildHamonics
HandleEvents
</syntaxhighlight>
{{output}}
<pre>
The first twenty harmonic numbers are:
1. 1.00000000
2. 1.50000000
3. 1.83333333
4. 2.08333333
5. 2.28333333
6. 2.45000000
7. 2.59285714
8. 2.71785714
9. 2.82896825
10. 2.92896825
11. 3.01987734
12. 3.10321068
13. 3.18013376
14. 3.25156233
15. 3.31822899
16. 3.38072899
17. 3.43955252
18. 3.49510808
19. 3.54773966
20. 3.59773966
The first harmonic number > 2 is 2.08333333 at position 4.
The first harmonic number > 3 is 3.01987734 at position 11.
The first harmonic number > 4 is 4.02724520 at position 31.
The first harmonic number > 5 is 5.00206827 at position 83.
The first harmonic number > 6 is 6.00436671 at position 227.
The first harmonic number > 7 is 7.00127410 at position 616.
The first harmonic number > 8 is 8.00048557 at position 1674.
The first harmonic number > 9 is 9.00020806 at position 4550.
The first harmonic number > 10 is 10.00004301 at position 12367.
</pre>
=={{header|Go}}==
Line 810 ⟶ 1,324:
3.05167e_6</syntaxhighlight>
=={{Header|Java}}==
Java does not have a built-in fraction type, so we create our own class Rational.
<syntaxhighlight lang="java">
import java.math.BigInteger;
public class HarmonicSeries {
public static void main(String[] aArgs) {
System.out.println("The first twenty Harmonic numbers:");
for ( int i = 1; i <= 20; i++ ) {
System.out.println(String.format("%2s", i) + ": " + harmonicNumber(i));
}
System.out.println();
for ( int i = 1; i <= 10; i++ ) {
System.out.print("The first term greater than ");
System.out.println(String.format("%2s%s%5s", i, " is Term ", indexedHarmonic(i)));
}
}
private static Rational harmonicNumber(int aNumber) {
Rational result = Rational.ZERO;
for ( int i = 1; i <= aNumber; i++ ) {
result = result.add( new Rational(BigInteger.ONE, BigInteger.valueOf(i)) );
}
return result;
}
private static int indexedHarmonic(int aTarget) {
BigInteger target = BigInteger.valueOf(aTarget);
Rational harmonic = Rational.ZERO;
BigInteger next = BigInteger.ZERO;
while ( harmonic.numerator.compareTo(target.multiply(harmonic.denominator)) <= 0 ) {
next = next.add(BigInteger.ONE);
harmonic = harmonic.add( new Rational(BigInteger.ONE, next) );
}
return next.intValueExact();
}
private static class Rational {
private Rational(BigInteger aNumerator, BigInteger aDenominator) {
numerator = aNumerator;
denominator = aDenominator;
BigInteger gcd = numerator.gcd(denominator);
numerator = numerator.divide(gcd);
denominator = denominator.divide(gcd);
}
@Override
public String toString() {
return numerator + " / " + denominator;
}
private Rational add(Rational aRational) {
BigInteger numer = numerator.multiply(aRational.denominator)
.add(aRational.numerator.multiply(denominator));
BigInteger denom = aRational.denominator.multiply(denominator);
return new Rational(numer, denom);
}
private BigInteger numerator;
private BigInteger denominator;
private static final Rational ZERO = new Rational(BigInteger.ZERO, BigInteger.ONE);
}
}
</syntaxhighlight>
{{ out }}
<pre>
The first twenty Harmonic numbers:
1: 1 / 1
2: 3 / 2
3: 11 / 6
4: 25 / 12
5: 137 / 60
6: 49 / 20
7: 363 / 140
8: 761 / 280
9: 7129 / 2520
10: 7381 / 2520
11: 83711 / 27720
12: 86021 / 27720
13: 1145993 / 360360
14: 1171733 / 360360
15: 1195757 / 360360
16: 2436559 / 720720
17: 42142223 / 12252240
18: 14274301 / 4084080
19: 275295799 / 77597520
20: 55835135 / 15519504
The first term greater than 1 is Term 2
The first term greater than 2 is Term 4
The first term greater than 3 is Term 11
The first term greater than 4 is Term 31
The first term greater than 5 is Term 83
The first term greater than 6 is Term 227
The first term greater than 7 is Term 616
The first term greater than 8 is Term 1674
The first term greater than 9 is Term 4550
The first term greater than 10 is Term 12367
</pre>
=={{header|jq}}==
Line 1,032 ⟶ 1,657:
First Harmonic > 10 is at position 12367 and is: 4534503430707033513455566663502488777398404081163864262146240513258488614453237798607335814524420102703735793862177214220961640516162786810577801568379848400841651563172393145644747756934779147852785761076984123029496399397933274328333851023356832490595994957906245622634743917027121730163673444620574773571394586325343348374089752330084853480910846154523214600594885010321970738793199335121376742737688996290912022884023314845989317485564897100378511371007284095835544913458386488350273752793299623280953681770210860670497293958742056567860493303919432966767309289555005524116155997967505009262492686887145801834344158217659625052992919107429112826740068763017007260951761133678087563009777021924759295735860359747992008280482368678698363760290512075843263479257144567423473653608660780306498167138240689075702661825821881383897412095062894498190524562267366610500376186508574923546863369628573748735962288669973834867370052620567124452691818158059495529870775349719430883965813897867964261906884105709015328654134185094852649077443558343796100212309241953109323566593312098467538550988320147927458982568637261872251614826312806756190545537354754639105220779296735305508074404777698608072480025436626465940783557587776095412527179972733639880928504521162532474790119331444432691186539731972229608857034838322577825073128558410147097241778325338487130870125908822766048925435961031468685135925285730005192072367106087421540485758689853548032678218115860840827961919559051579906147674926980159462587970312884204058339415498440724533667854443260894961415867322707773766644126293587970041291934576744798355640180480297466389631305725091134483147261680364583681456904845585042916227359755995566890651618068412417567353169223028238974716410284035466524218357680139996958854138926338447160349489618026519182480829051291094774428369589524841439952414899018430629415759045664629576805779430276126299459472265505596409675499333035181404107887631586541773720233030773460233097013905563454586768052944023799630803277004868637818739278212959623313318901685226624666106128149541383179968968079822908437213133926503243634564555471480742603760558963949447568409555153275556694530840495402464574679819190097934082680991390359677270683921719809487985411431453913318562222280325934810896976109622317012462673397599719705029993095451945802745111845994127113737531302666646673629309399879563721820841693763990040297218084280469660603933736914103580592334169009905536955683757799785465521029810481052093318974648597912401819690931945953441013940611090922220615447632315575131416623986489801748397222861527442923686453815927754305883939843644528744788311441317667800082400625247002131690240576547715553985566084722165603169180546444489624520529458589659642945674302803518493446186365401036652868957343947436300845516052248544996767002703372227801331704347861429376714087429190841582994100706608870432263478840976847125656598528047665054259600221287735441697634905261794158123419440836603187910006400385658161609560077480916666767855249401496376453813742910897685304674607932781480153350592305086143517293124048321908049033338641165570949920967640973467814840149770609739430967880836391708342980969076413706547475361151566568646558729953788076269958878680638806411347398270002468450490060229923546495153668589442405650268354841362770166414940668952342796856334297184594689014220369402540999903691567293267477507617730573216005494288894386265419609930709688051786459868855999927483488595292377625472492052607166011299662062394773003492445503755319504334407628427786801438298993197490802949903537017176795900523366221528304387658556186131452558642788326427005831945047208416461903276903155157668071084197085232239303753932511966601799642086840010635787283417484115163601638040747720429853554897965062666245152120838888282696144547158569268308151508594359471912253952609211269960896327745083608820919865564411609729050094802982153483731969811821363213666501089803250069914862591069398131811421717727581994465281157595132213790173740210606315458787942312889500024592644472634497210343312196800423898410785211559075127039914648882418769844305126070628158439406823975898202123936987508547712323439814808927188496139029784726424065836399799566957465329325900733347158011735890776039622239371179265322102988095792334295987922829904316643744024475158366697011639022690011158534933281478551427221827338035502405739017675964995339845575688974247145430375550691172792583150675040459847494992816879937873922797432917540308251685230808170901253598248750205022912447198383112847277587880630475986296945942943527602129139602849994318853893879911800330577976183782475767979870512555206262710949997353103772493020471652674012338306053325512634115113811440908388247422072755018950413835394298503429471638926223466724120693416489874608276360557167546047009826979490836032462574788898996808959092152232893733971469326230223411125857734727852907092167761679250398986918637504310219629562470003641972668110649513078347115663607119611611006136091187311740932841583114177470218100285066869010543963406829140648421377028252417899384810247910009920738953581331407151723899810868371969278374342093106625781466735739058011357436506412309273928847791977164882301609474829416331188046487042397727216661613196578592821103409588225020153177686173957843637300970946602788598104463189226384477573248319694609//453448392867348851861091842716460781522665326792904183722427862157021725614855278045402902750948524499248477906574954049723047247594567849381505559142259985012563911748565504645288824396149684911357398473040997444532446072249205183698951114867996915790953480940595875198164176514792266197724950029214098402750523319656510658391308781455532640143957171928728555028441113976098936445243888308518334732068287540969911145046182240997844332542069999808052999118116686423274752490237063716145951662497086525502824771022018772683298755747961799756488875473662436395793972289765688786340400767092625088976215404821615642169932407067470102277881619113300360581665503419953488853618786486589079218434762164433122957020446969147378233696729003877954852548129234246125950262402365717815616819562222237997997268259525610560218332639694073974306248739683910746615242978454786299588282966741711638421737040643849869111250119460946958342235754393754105273921365540335675025520532198380359075366480578543033141107171068864236199764731934475297409089137917767464818172280194587098425992699315337227143311157563983501099319586806728853272646048761957836787873218028733894581386787413379357471544256309173104246757027297103897425448969584443551192032578044112779996916037308469908337849261001566062681902158730668479447685029245562145758050351907230317974951652391896463264624212612669169958584934650809482293303230830931776045695753750127961326467827548499522738908622830870349146611375298940888140985679637170914965525299929769378946655485787070387076631251882242836138520842058399796780766046354724533075054753447434289238707943437708102115231865561988793697866081966627386198255657705081440529935972313855299293571946459814547702790931940409505592380201618395383529120246923953942192402976907753500903555076008341911303039471562108255892056978939810785607998919899547795388848467866707335193584754101418435349055093490132220307797847159336930832196642264566173052472986519467903662478761577267524782906438677344301510628707749510764610883151848961955324250103497542040100381108000294328086486819670637824004877822719162400898805753721906246725669673698667303029853553151086095673161642688637369399134211142673038004309271354569340138672196310045673847468188540492497939082450727559160669323441829424345229568861519806871166312840505922345924286612289038405635960847312841549454914894505350287965178933448588642960151653234597627993111784598027362458363048975481887472153211279255977999546404147533745281771529556720982887239728930885170033344102088264480888466142172463254195760915805324061034675182591049442628706041312626422073008073380371673927489824737483560681019534670531017902066234272224653619745905599447903061483059896873406142453228071022111502256443781491460846164401184358168702828324631516293734123540067969597713270070892954605122527765020904360443840604089525630920883767509762055795186065284871898250633904172393012014014535429691316180843284005611214029789777910907448104608381684001408038080004630598753746420393898907687445970436071633844317405361945225336609003279748456376641015025188398108421593478229298294410838458456380669395413849296975844767158362010790056013282230712593275083853985899993525361915338786353135213679507571177474865535450360805151635896650877459021597451290179824388706852573538022338292357056094650723608655495776391045556275691435553166984429143943751883621223890112143444263384709343311021515999913133625576607936737600163990937589076505709728288249796177860701551483858105729270343952736046045949895941189683687455280876075868089128908950093274631325285867675575977007649875882080181911556426324514888965309812114552424769046963560561519998228670210152775853158532301504121266893422531369102008133615525509443494794446512860320064722889237146201868974019228593633572436903033783142941154726917069945760001298893890438043207045074201509279648515350335803482110210899536912444564551795055524051376159340142763939561343534419114897944064189816231618709358147206686123692571007252707031453516920926510941282670271991207431645277787732194166279571541705091430384118591739755560716583929251984774474735360846706097322805037517607175954157003966139895604444104180849566439510557422016972444504568924435928285183045942516523723723922905128092098303510237702313418511361585451364656754043639465582976252775658243115735311521322732866960027744814046142646066362389168699571924976468952738225372771528877335171820809981966462557399840199438944317868064756592423558340956344597149662019813621964301710551795219655353560019310354145741006960293249850509760942103140771516196121166914225789961295123942408454678165630224229246096815718964524008072338418161910957019466321162530778568751489056122708488740001553449809520216651409154456422832210306621326600466249277216434300763703544991709516688672829002850684750220066717750016340009488155733886564204666531055424099636022638066094074880147267683122477920693324135470681030117673286007072403853987896516881673522241375339519109365317259361633140780497503747668264390394453428165247265288377265912593743778917613302228374835985611202269353962434983431127134732498447341566434664481796653135468887881140453881191678527573715771628361883084372307861539269288978542389654945192750390734178119092263987452761982138487929715357003527512352779194620327380792004034424949320206418355200000
</pre>
=={{header|Lua}}==
<syntaxhighlight lang="lua">-- Task 1
function harmonic (n)
if n < 1 or n ~= math.floor(n) then
error("Argument to harmonic function is not a natural number")
end
local Hn = 1
for i = 2, n do
Hn = Hn + (1/i)
end
return Hn
end
-- Task 2
for x = 1, 20 do
print(x .. " :\t" .. harmonic(x))
end
-- Task 3
local x, lastInt, Hx = 0, 1
repeat
x = x + 1
Hx = harmonic(x)
if Hx > lastInt then
io.write("The first harmonic number above " .. lastInt)
print(" is " .. Hx .. " at position " .. x)
lastInt = lastInt + 1
end
until lastInt > 10 -- Stretch goal just meant changing that value from 5 to 10
-- Execution still only takes about 120 ms under LuaJIT</syntaxhighlight>
{{out}}
<pre>1 : 1
2 : 1.5
3 : 1.8333333333333
4 : 2.0833333333333
5 : 2.2833333333333
6 : 2.45
7 : 2.5928571428571
8 : 2.7178571428571
9 : 2.8289682539683
10 : 2.9289682539683
11 : 3.0198773448773
12 : 3.1032106782107
13 : 3.1801337551338
14 : 3.2515623265623
15 : 3.318228993229
16 : 3.380728993229
17 : 3.4395525226408
18 : 3.4951080781963
19 : 3.5477396571437
20 : 3.5977396571437
The first harmonic number above 1 is 1.5 at position 2
The first harmonic number above 2 is 2.0833333333333 at position 4
The first harmonic number above 3 is 3.0198773448773 at position 11
The first harmonic number above 4 is 4.0272451954365 at position 31
The first harmonic number above 5 is 5.0020682726802 at position 83
The first harmonic number above 6 is 6.0043667083456 at position 227
The first harmonic number above 7 is 7.0012740971342 at position 616
The first harmonic number above 8 is 8.0004855719958 at position 1674
The first harmonic number above 9 is 9.0002080629311 at position 4550
The first harmonic number above 10 is 10.000043008276 at position 12367</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
Line 1,040 ⟶ 1,728:
<pre>{1, 3/2, 11/6, 25/12, 137/60, 49/20, 363/140, 761/280, 7129/2520, 7381/2520, 83711/27720, 86021/27720, 1145993/360360, 1171733/360360, 1195757/360360, 2436559/720720, 42142223/12252240, 14274301/4084080, 275295799/77597520, 55835135/15519504}
{2, 4, 11, 31, 83, 227, 616, 1674, 4550, 12367}</pre>
=={{header|Maxima}}==
<syntaxhighlight lang="maxima">
harmonic(n):=apply("+",1/makelist(i,i,n))$
first_greater_than_n(len):=block(i:1,result:[],while harmonic(i)<=len do (result:endcons(i,result),i:i+1),last(result)+1)$
/* Test cases */
/* First 20 harmonic numbers */
makelist(harmonic(j),j,20);
/* First harmonic number that exceeds a positive integer from 1 to 5 */
makelist(first_greater_than_n(k),k,5);
</syntaxhighlight>
{{out}}
<pre>
[1,3/2,11/6,25/12,137/60,49/20,363/140,761/280,7129/2520,7381/2520,83711/27720,86021/27720,1145993/360360,1171733/360360,1195757/360360,2436559/720720,42142223/12252240,14274301/4084080,275295799/77597520,55835135/15519504]
[2,4,11,31,83]
</pre>
=={{header|Nim}}==
Line 1,811 ⟶ 2,519:
</pre>
=={{header|RPL}}==
≪ 0 1 ROT '''FOR''' j INV + '''NEXT''' ≫ ‘'''HARMO'''’ STO
≪ 5 FIX { } 1 20 '''FOR''' n n + '''HARMO NEXT''' ≫ EVAL
{{out}}
<pre>
1: { 1.00000 1.50000 1.83333 2.08333 2.28333 2.45000 2.59286 2.71786 2.82897 2.92897 3.01988 3.10321 3.18013 3.25156 3.31823 3.38073 3.43955 3.49511 3.54774 3.59774 }
</pre>
We haved fulfilled the stretched part of the task on a vintage HP-28S, with the objective to be as fast as possible. H(n+1) is calculated directly from H(n), and a <code>FOR..NEXT</code> loop allows to reduce stack depth and eliminate the counter incrementation by the user; 9999 is a magic number used to exit the loop.
≪ → max
≪ { } 0 1 9999 '''FOR''' j
j INV +
'''IF''' OVER SIZE 1 + OVER <
'''THEN''' SWAP j +
'''IF''' DUP SIZE max > '''THEN''' 9999 'j' STO '''END'''
SWAP '''END'''
'''NEXT''' DROP
≫ ≫ ‘'''TASK2'''’ STO
{{out}}
<pre>
1: { 2 4 11 31 83 227 616 1674 4550 12367 }
</pre>
was returned in less than 8 minutes.
=={{header|Ruby}}==
<syntaxhighlight lang="ruby">harmonics = Enumerator.new do |y|
res = 0
(1..).each {|n| y << res += Rational(1, n) }
end
n = 20
The first #{n} harmonics (as rationals):""
harmonics.take(n).each_slice(5){|slice| puts "%20s"*slice.size % slice }
puts
milestones = (1..10).to_a
harmonics.each.with_index(1) do |h,i|
if h > milestones.first then
puts "The first harmonic number > #{milestones.shift} is #{h.to_f} at position #{i}"
end
break if milestones.empty?
end
</syntaxhighlight>
{{out}}
<pre> 1/1 3/2 11/6 25/12 137/60
49/20 363/140 761/280 7129/2520 7381/2520
83711/27720 86021/27720 1145993/360360 1171733/360360 1195757/360360
2436559/720720 42142223/12252240 14274301/4084080 275295799/77597520 55835135/15519504
The first harmonic number > 1 is 1.5 at position 2
The first harmonic number > 2 is 2.0833333333333335 at position 4
The first harmonic number > 3 is 3.019877344877345 at position 11
The first harmonic number > 4 is 4.02724519543652 at position 31
The first harmonic number > 5 is 5.002068272680166 at position 83
The first harmonic number > 6 is 6.004366708345566 at position 227
The first harmonic number > 7 is 7.001274097134161 at position 616
The first harmonic number > 8 is 8.00048557199578 at position 1674
The first harmonic number > 9 is 9.00020806293114 at position 4550
The first harmonic number > 10 is 10.000043008275808 at position 12367
</pre>
=={{header|Rust}}==
Using big rationals and big integers from the [https://docs.rs/num/latest/num/ num] crate.
Line 1,816 ⟶ 2,585:
use num::rational::Ratio;
use num::BigInt;
use std::num::NonZeroU64;
fn main() {
for n in 1..=20 {
// `harmonic_number` takes the type `NonZeroU64`,
// which is just a normal u64 which is guaranteed to never be 0.
// We convert n into this type with `n.try_into().unwrap()`,
// where the unwrap is okay because n is never 0.
println!(
"Harmonic number {n} = {}",
harmonic_number(n.try_into().unwrap())
);
}
// The unwrap here is likewise okay because 100 is not 0.
println!(
"Harmonic number 100 = {}",
harmonic_number(100.try_into().unwrap())
);
// In order to avoid recomputing all the terms in the sum for every harmonic number
// we save the value of the harmonic series between loop iterations
// and just add 1/iter to it.
let mut target = 1;
Line 1,838 ⟶ 2,619:
}
// Compute the next term in the harmonic series.
iter += 1;
harmonic_number += Ratio::from_integer(iter.into()).recip();
Line 1,844 ⟶ 2,625:
}
fn harmonic_number(n:
// Convert each integer from 1 to n into an arbitrary precision rational number
// and sum their reciprocals.
(1..=n
.map(|i| Ratio::from_integer(i.into()).recip())
.sum()
}
</syntaxhighlight>
Line 1,885 ⟶ 2,668:
Position of first term > 10 is 12367
</pre>
=={{header|Tcl}}==
<syntaxhighlight lang="tcl># Task 1
proc harmonic {n} {
if {$n < 1 || $n != [expr {floor($n)}]} {
error "Argument to harmonic function is not a natural number"
}
set Hn 1
for {set i 2} {$i <= $n} {incr i} {
set Hn [expr {$Hn + (1.0/$i)}]
}
return $Hn
}
# Task 2
for {set x 1} {$x <= 20} {incr x} {
set Hx [harmonic $x]
puts "$x: $Hx"
}
# Task 3 /stretch
set x 0
set lastInt 1
while {$lastInt <= 10} {
incr x
set Hx [harmonic $x]
if {$Hx > $lastInt} {
puts -nonewline "The first harmonic number above $lastInt"
puts " is $Hx at position $x"
incr lastInt
}
}
</syntaxhighlight>
{{out}}
<pre>1: 1
2: 1.5
3: 1.8333333333333333
4: 2.083333333333333
5: 2.283333333333333
6: 2.4499999999999997
7: 2.5928571428571425
8: 2.7178571428571425
9: 2.8289682539682537
10: 2.9289682539682538
11: 3.0198773448773446
12: 3.103210678210678
13: 3.180133755133755
14: 3.251562326562327
15: 3.3182289932289937
16: 3.3807289932289937
17: 3.439552522640758
18: 3.4951080781963135
19: 3.547739657143682
20: 3.597739657143682
The first harmonic number above 1 is 1.5 at position 2
The first harmonic number above 2 is 2.083333333333333 at position 4
The first harmonic number above 3 is 3.0198773448773446 at position 11
The first harmonic number above 4 is 4.02724519543652 at position 31
The first harmonic number above 5 is 5.002068272680166 at position 83
The first harmonic number above 6 is 6.004366708345567 at position 227
The first harmonic number above 7 is 7.001274097134162 at position 616
The first harmonic number above 8 is 8.000485571995782 at position 1674
The first harmonic number above 9 is 9.000208062931115 at position 4550
The first harmonic number above 10 is 10.000043008275778 at position 12367</pre>
=={{header|Verilog}}==
Line 1,918 ⟶ 2,765:
{{libheader|Wren-big}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="
import "./fmt" for Fmt
var harmonic = Fn.new { |n| (1..n).reduce(BigRat.zero) { |sum, i| sum + BigRat.one/i } }
| |||