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Search: id:A099358
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| A099358 |
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a(n) = sum of digits of k^4 as k runs from 1 to n. |
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+0
1
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| 1, 8, 17, 30, 43, 61, 68, 87, 105, 106, 122, 140, 162, 184, 202, 227, 246, 273, 283, 290, 317, 339, 370, 397, 422, 459, 477, 505, 530, 539, 561, 592, 619, 644, 663, 699, 727, 752, 770, 783, 814, 841, 866, 903, 921, 958, 1001, 1028, 1059, 1072, 1099, 1124, 1161
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = a(n-1) + sum of decimal digits of n^4.
a(n)=sum(k=1, n, sum(m=0, floor(log(k^4)), floor(10((k^4)/(10^(((floor(log(k^4))+1))-m)) - floor ((k^4)/(10^(((floor(log(k^4))+1))-m)))))))
General formula: a(n)_p = sum(k=1, n, sum(m=0, floor(log(k^p)), floor(10((k^p)/(10^(((floor(log(k^p))+1))-m)) - floor ((k^p)/(10^(((floor(log(k^p))+1))-m))))))). Here a(n)_p is a sum of digits of k^p from k=1 to n
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EXAMPLE
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a(600)=sum(k=1,600,sum(m=0,floor(log(k^4)),floor(10*((k^4)/(10^(((floor(log(k^4))+1))-m)) - floor ((k^4)/(10^(((floor(log(k^4))+1))-m)))))))=23812 => a(600)=23812 = a(600)_4 because p=4
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MATHEMATICA
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f[n_] := Block[{s = 0, k = 1}, While[k <= n, s = s + Plus @@ IntegerDigits[k^4]; k++ ]; s]; Table[ f[n], {n, 50}] (from Robert G. Wilson v Nov 18 2004)
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CROSSREFS
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Cf. k^1 in A037123, k^2 in A071317 & k^3 in A071121.
Adjacent sequences: A099355 A099356 A099357 this_sequence A099359 A099360 A099361
Sequence in context: A044441 A056121 A028884 this_sequence A077222 A077221 A106648
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KEYWORD
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nonn,easy,base
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AUTHOR
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Aktir Yalcin (aktaryalcin(AT)msn.com), Nov 16 2004
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EXTENSIONS
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Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 18 2004
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