cp's OEIS Frontend

A283034 Numbers k such that k = (sum of digits of k)^(last digit of k).

%I A283034 #20 Jul 24 2021 01:11:35
%S A283034 1,4913,19683,52521875,24794911296,68719476736,271818611107,
%T A283034 1174711139837
%N A283034 Numbers k such that k = (sum of digits of k)^(last digit of k).
%C A283034 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).
%e A283034 1 = 1^1,
%e A283034 4913 = (4+9+1+3)^3,
%e A283034 19683 = (1+9+6+8+3)^3,
%e A283034 52521875 = (5+2+5+2+1+8+7+5)^5.
%t A283034 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 *)
%o A283034 (VBA)
%o A283034 Sub calcul()
%o A283034    Sheets("Result").Select
%o A283034    Range("A1").Select
%o A283034    For i = 1 To 10000000
%o A283034       Sum = 0
%o A283034       For k = 1 To Len(i)
%o A283034          Sum = Sum + Mid(i, k, 1)
%o A283034       Next
%o A283034       If Sum ^Mid(i, len(i), 1)= i Then
%o A283034          ActiveCell.Value = i
%o A283034          ActiveCell.Offset(1, 0).Select
%o A283034       End If
%o A283034    Next
%o A283034 End Sub
%Y A283034 Cf. A007953, A010879, A023106.
%K A283034 nonn,base,fini,full
%O A283034 1,2
%A A283034 _Shmelev Aleksei_, Feb 27 2017
%E A283034 a(5)-a(8) from _Giovanni Resta_, Feb 27 2017