Hickerson series of almost integers: Difference between revisions
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m (→version 2: changed height of the output section window.) |
m (→version 2: added whitespace, simplified the wording in the REXX section header.) |
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===version 2=== |
===version 2=== |
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This REXX version can calculate the Hickerson series to any number up to the length (in decimal digits) |
This REXX version can calculate the Hickerson series to any number up to the length (in decimal digits) |
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<br> |
<br>of the number returned by the '''ln2''' function. |
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This version supports up to '''507''' decimal digits. |
This version supports up to '''507''' decimal digits. |
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<lang rexx>/*REXX program to calculate and show the Hickerson series (are near integer). */ |
<lang rexx>/*REXX program to calculate and show the Hickerson series (are near integer). */ |
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numeric digits length(ln2()) |
numeric digits length(ln2())-length(.) /*be able to calculate big factorials. */ |
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parse arg N . /*get optional number of values to use.*/ |
parse arg N . /*get optional number of values to use.*/ |
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if N=='' then N= |
if N=='' then N= 1 /*Not specified? Then use the default.*/ |
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/* [↓] compute possible Hickerson #s. */ |
/* [↓] compute possible Hickerson #s. */ |
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do j=1 for N; #=Hickerson(j) |
do j=1 for N; #= Hickerson(j) /*traipse thru a range of Hickerson #s.*/ |
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?=right(#*10%1, 1) |
?= right(# * 10 % 1, 1) /*get 1st decimal digit past dec. point*/ |
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if ?==0 | ?==9 then _= 'almost integer' /*the number is, */ |
if ?==0 | ?==9 then _= 'almost integer' /*the number is, */ |
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else _= ' ' /* or it ain't. */ |
else _= ' ' /* or it ain't. */ |
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say right(j,3) _ format(#,,5) |
say right(j,3) _ format(#, , 5) /*show number with 5 dec digs fraction.*/ |
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end /*j*/ |
end /*j*/ |
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exit /*stick a fork in it, we're all done. */ |
exit /*stick a fork in it, we're all done. */ |
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/*─────────────────────────────────────────────────────────────────────────────────────────────────────────*/ |
/*─────────────────────────────────────────────────────────────────────────────────────────────────────────*/ |
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!: procedure; parse arg x; !=1; |
!: procedure; parse arg x; !=1; do j=2 to x; != !*j; end; return ! /* ◄──compute X factorial*/ |
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Hickerson: procedure; parse arg z; |
Hickerson: procedure; parse arg z; return !(z) / (2*ln2() ** (z+1)) |
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ln2: return .69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641, |
ln2: return .69314718055994530941723212145817656807550013436025525412068000949339362196969471560586332699641, |
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|| 8687542001481020570685733685520235758130557032670751635075961930727570828371435190307038623891673471123, |
|| 8687542001481020570685733685520235758130557032670751635075961930727570828371435190307038623891673471123, |
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