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 A259313 Numbers n for which there exists a k>=2 such that n equals the average of digitsum(n^p) for p from 1 to k. 1
 1, 9, 12, 13, 16, 19, 21, 49, 61, 67, 84, 106, 160, 191, 207, 250, 268, 373, 436, 783, 2321, 3133, 3786, 3805, 4842, 5128, 8167, 13599, 29431, 35308 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Digitsum = (A007953). The 'k's are 2, 2, 4, 3, 4, 5, 7, 12, 15, 16, 19, 21, 57, 37, 38, 79, 48, 63, 72, 119, 306, 397, 469, 472, 582, 613, 927, 1461, 2926, 3449, ..., . - Robert G. Wilson v, Jul 30 2015 LINKS EXAMPLE Digitsum(9) is 9, digitsum(9^2) is 9. (9+9)/2 = 9. So 9 is in this sequence. 12^1 = 12, 12^2 = 144, 12^3 = 1728 and 12^4 = 20736. Digitsum(12) = 3, digitsum(144) = 9, digitsum(1728) = 18, digitsum(20736) = 18, (3+9+18+18)/4 = 12. So 12 is in this sequence. MATHEMATICA fQ[n_] := If[ IntegerQ@ Log10@ n, False, Block[{pwr = 2, s = Plus @@ IntegerDigits@ n}, While[s = s + Plus @@ IntegerDigits[n^pwr]; s < n*pwr, pwr++]; If[s == n*pwr, True, False]]]; k = 1; lst = {1}; While[k < 100001, If[fQ@ k, AppendTo[lst, k]]; k++]; lst (* Robert G. Wilson v, Jul 30 2015 *) PROG (Python) def sod(n): ....kk = 0 ....while n > 0: ........kk= kk+(n%10) ........n =int(n//10) ....return kk for c in range (2, 10**4): ....bb=0 ....for a in range(1, 200): ........bb=bb+sod(c**a, 10) ........if bb==c*a: ............print (c, a) CROSSREFS Cf. A007953, A061910, A061209, A061210. Sequence in context: A335168 A295486 A032687 * A170951 A044859 A336754 Adjacent sequences:  A259310 A259311 A259312 * A259314 A259315 A259316 KEYWORD nonn,base,more AUTHOR Pieter Post, Jun 24 2015 EXTENSIONS a(21)-a(28) from Giovanni Resta, Jun 24 2015 a(1)-a(28) checked by Robert G. Wilson v, Jul 30 2015 a(29)-a(30) from Robert G. Wilson v, Jul 30 2015 STATUS approved

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Last modified June 24 21:50 EDT 2021. Contains 345433 sequences. (Running on oeis4.)