A099358 a(n) = sum of digits of k^4 as k runs from 1 to n.

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

Offset: 1

Author

Yalcin Aktar, Nov 16 2004

Keywords

• nonn
• easy
• base

Comments

Partial sums of A055565.

Examples

			a(3) = sum_digits(1^4) + sum_digits(2^4) + sum_digits(3^4) = 1 + 7 + 9 = 17.
		

Crossrefs

Cf. k^1 in A037123, k^2 in A071317 & k^3 in A071121.

Programs

Mathematica

f[n_] := Block[{s = 0, k = 1}, While[k <= n, s = s + Plus @@ IntegerDigits[k^4]; k++ ]; s]; Table[ f[n], {n, 50}] (* Robert G. Wilson v, Nov 18 2004 *)
Accumulate[Table[Total[IntegerDigits[n^4]],{n,60}]] (* Harvey P. Dale, Jun 08 2021 *)

Formula

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.

Extensions

Edited and extended by Robert G. Wilson v, Nov 18 2004

Existing example replaced with a simpler one by Jon E. Schoenfield, Oct 20 2013