A266818 Consider a number x = concat(a,b). Sequence lists numbers x such that digits of b^a end in x.

25, 96, 296, 568, 625, 696, 776, 1296, 1616, 3125, 3251, 4656, 5625, 5696, 6128, 6192, 6576, 7749, 9776, 17568, 26241, 34375, 40625, 47749, 51469, 51821, 53125, 56251, 58307, 59776, 61376, 65625, 71296, 71299, 71301, 71875, 76481, 86976, 90625, 99499, 99501, 109376

Offset

1,1

Comments

25: 5^2 = 25;

96: 6^9 = 10077696 that ends in 96;

296: 6^29 = 36845653286788892983296 that ends in 296;

3125: 125^3 = 1953125 that ends in 3125.

Links

Table of n, a(n) for n=1..42.

Maple

with(numtheory): P:= proc(q) local a, b, c, d, k, n;
for n from 10 to q do d:=ilog10(n); for k from 1 to d do a:=(n mod 10^k)^trunc(n/10^k); b:=ilog10(a)+1;
if a mod 10^(d+1)=n then print(n); break; fi; od; od; end: P(10^6);

Mathematica

Select[Range@ 110000, AnyTrue[Function[n, FromDigits@ If[Length@ # < IntegerLength@ n, #, Take[#, -IntegerLength@ n]] &@ IntegerDigits[#2^#1] & @@@ Map[Function[k, Map[FromDigits, TakeDrop[#, k]]], Range[Length@ # - 1]] &@ IntegerDigits@ n]@ #, Function[m, m == #]] &] (* Michael De Vlieger, Jan 14 2016 *)

Crossrefs

Cf. A266817, A273382, A273383.

Sequence in context: A256716 A063769 A099771 * A158547 A144854 A237202

Adjacent sequences: A266815 A266816 A266817 * A266819 A266820 A266821

Keyword

nonn,base

Author

Paolo P. Lava, Jan 04 2016

Status

approved