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 A283034 Numbers k such that k = (sum of digits of k)^(last digit of k). 0
 1, 4913, 19683, 52521875, 24794911296, 68719476736, 271818611107, 1174711139837 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The check must be done up to 10^22 (then for 23 digits in a number max result can be (23*10)^9 = 4, 6*10^20 < 10^22). LINKS Table of n, a(n) for n=1..8. EXAMPLE 1 = 1^1, 4913 = (4+9+1+3)^3, 19683 = (1+9+6+8+3)^3, 52521875 = (5+2+5+2+1+8+7+5)^5. MATHEMATICA Union[Reap[nd=1; Sow[1]; While[Ceiling[(10^(nd-1))^(1/9)] <= 9 nd, Do[ Do[v = s^e; If[Mod[v, 10] == e && Plus @@ IntegerDigits@ v == s, Sow[v]], {s, Ceiling[ (10^(nd-1))^(1/e)], Min[ Floor[10^(nd/e)], 9 nd]}], {e, 2, 9}]; nd++]][[2, 1]]] (* all terms, Giovanni Resta, Feb 27 2017 *) PROG (VBA) Sub calcul() Sheets("Result").Select Range("A1").Select For i = 1 To 10000000 Sum = 0 For k = 1 To Len(i) Sum = Sum + Mid(i, k, 1) Next If Sum ^Mid(i, len(i), 1)= i Then ActiveCell.Value = i ActiveCell.Offset(1, 0).Select End If Next End Sub CROSSREFS Cf. A007953, A010879, A023106. Sequence in context: A179144 A036530 A088069 * A114770 A013807 A013884 Adjacent sequences: A283031 A283032 A283033 * A283035 A283036 A283037 KEYWORD nonn,base,fini,full AUTHOR Shmelev Aleksei, Feb 27 2017 EXTENSIONS a(5)-a(8) from Giovanni Resta, Feb 27 2017 STATUS approved

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Last modified July 22 00:08 EDT 2024. Contains 374478 sequences. (Running on oeis4.)