Goodstein Sequence: Difference between revisions
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→{{header|Wren}}: Updated in line with Julia example of which it is a translation. |
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Term 15 of Goodstein(15): 14063084452070776884879 |
Term 15 of Goodstein(15): 14063084452070776884879 |
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Term 16 of Goodstein(16): 2771517379996516970665566613559367879596937714713289695169887161862950129194382447127464877388711781205972046374648603545513430106433206876557475731408608398953667881600740852227698037876781766310900319669456854530159244376159780346700931210394158247781113134808720678004134212529413831368888355854503034587880113970541681685966414888841800498150131839091463034162026108960280455620621355407543489960326268155088833218122810217973039385643494213235664908254695964740257569988152978579630435471016976693529875691083071137361386386918409765002837648351746984484967203877495399596876291343126699827442908994036031608979805166915596436929638418152127561722561465793969723556331679336828840983098559789555364076924597258115780567651772009250336359472037679350612341393780002377587368649157608579801815531133644879180066181854487069796160774056572568941004114162614925 |
Term 16 of Goodstein(16): 2771517379996516970665566613559367879596937714713289695169887161862950129194382447127464877388711781205972046374648603545513430106433206876557475731408608398953667881600740852227698037876781766310900319669456854530159244376159780346700931210394158247781113134808720678004134212529413831368888355854503034587880113970541681685966414888841800498150131839091463034162026108960280455620621355407543489960326268155088833218122810217973039385643494213235664908254695964740257569988152978579630435471016976693529875691083071137361386386918409765002837648351746984484967203877495399596876291343126699827442908994036031608979805166915596436929638418152127561722561465793969723556331679336828840983098559789555364076924597258115780567651772009250336359472037679350612341393780002377587368649157608579801815531133644879180066181854487069796160774056572568941004114162614925 |
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</pre> |
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=={{header|Phix}}== |
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Modified version of the python code from A059934 - tbh, I did not expect to get anywhere near this far using native atoms, |
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and always planned to write a gmp version, but now that just feels like too much effort for too little gain. |
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<syntaxhighlight lang="phix"> |
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function digits(atom n, b) |
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-- least significant first, eg 123,10 -> {3,2,1} or 6,2 -> {0,1,1} |
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sequence r = {remainder(abs(n),b)} |
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while n>=b do |
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n = floor(n/b) |
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r &= remainder(n,b) |
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end while |
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return r |
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end function |
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function bump(atom n, b) |
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atom res = 0 |
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for i,d in digits(n,b) do |
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if d then |
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res += d*power(b+1,bump(i-1,b)) |
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end if |
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end for |
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return res |
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end function |
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function A059934(atom n, k) |
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for i=1 to k do |
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n = bump(n, i+1)-1 |
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end for |
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return n |
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end function |
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function goodstein(atom n, maxterms = 10) |
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sequence res = {n} |
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while length(res)<maxterms and res[$]!=0 do |
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res &= A059934(n,length(res)) |
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end while |
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return res |
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end function |
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printf(1,"Goodstein(n) sequence (first 10) for values of n from 0 through 7:\n") |
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for i=0 to 7 do |
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printf(1,"Goodstein of %d: %v\n",{i,goodstein(i)}) |
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end for |
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printf(1,"\n") |
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printf(1,"The Nth term of Goodstein(N) sequence counting from 0, for values of N from 0 through 16:\n") |
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bool m64 = machine_bits()=64 |
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for i=0 to iff(m64?16:15) do |
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string ia = iff(i>=iff(m64?13:12)?" (inaccurate)":""), |
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gs = shorten(sprintf("%d",goodstein(i,i+1)[$])) |
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printf(1,"Term %d of Goodstein(%d): %s%s\n",{i,i,gs,ia}) |
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end for |
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</syntaxhighlight> |
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{{out}} (on 64-bit) |
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<pre> |
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Goodstein(n) sequence (first 10) for values of n from 0 through 7: |
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Goodstein of 0: {0} |
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Goodstein of 1: {1,0} |
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Goodstein of 2: {2,2,1,0} |
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Goodstein of 3: {3,3,3,2,1,0} |
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Goodstein of 4: {4,26,41,60,83,109,139,173,211,253} |
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Goodstein of 5: {5,27,255,467,775,1197,1751,2454,3325,4382} |
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Goodstein of 6: {6,29,257,3125,46655,98039,187243,332147,555551,885775} |
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Goodstein of 7: {7,30,259,3127,46657,823543,16777215,37665879,77777775,150051213} |
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The Nth term of Goodstein(N) sequence counting from 0, for values of N from 0 through 16: |
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Term 0 of Goodstein(0): 0 |
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Term 1 of Goodstein(1): 0 |
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Term 2 of Goodstein(2): 1 |
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Term 3 of Goodstein(3): 2 |
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Term 4 of Goodstein(4): 83 |
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Term 5 of Goodstein(5): 1197 |
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Term 6 of Goodstein(6): 187243 |
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Term 7 of Goodstein(7): 37665879 |
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Term 8 of Goodstein(8): 20000000211 |
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Term 9 of Goodstein(9): 855935016215 |
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Term 10 of Goodstein(10): 44580503598539 |
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Term 11 of Goodstein(11): 2120126221988686 |
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Term 12 of Goodstein(12): 155568095557812625 |
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Term 13 of Goodstein(13): 6568408355712901452 (inaccurate) |
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Term 14 of Goodstein(14): 295147905179358418240 (inaccurate) |
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Term 15 of Goodstein(15): 14063084452070776847260 (inaccurate) |
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Term 16 of Goodstein(16): 27715173799965170860...62604488626682848248 (862 digits) (inaccurate) |
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</pre> |
</pre> |
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