A266817 - OEIS

A266817

Numbers x = concat(a,b) such that b^a begins with the digits of x.

25, 59, 102, 104, 250, 590, 1306, 1976, 2500, 3763, 12998, 13060, 19760, 21912, 25000, 53216, 71457, 73365, 137083, 143507, 214651, 250000, 348611, 609185, 732021, 2500000, 3323935, 3486110, 7848843, 12122159, 19977668, 25000000, 59725459, 117927427, 128226908

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OFFSET

1,1

COMMENTS

Any numbers of the form 25*10^k, with k>=0, are part of the sequence.

LINKS

Table of n, a(n) for n=1..35.

EXAMPLE

25: 5^2 = 25;

59: 9^5 = 59049 that begins with 59;

102: 2^10 = 1024 that begins with 102;

1306: 6^13 = 13060694016 that begins with 1306;

3763: 63^37 = 3763572874813444727106020660762327844147969869582735798064027429183 that begins with 3763.

MAPLE

with(numtheory): P:= proc(q) local a, b, c, d, k, n;

for n from 1 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 trunc(a/10^(b-d-1))=n then print(n); break; fi; od; od; end: P(10^6);

MATHEMATICA

Select[Range[10^5], 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 12 2016, Version 10.2 *)

CROSSREFS

Cf. A273382, A266818, A273383.

Sequence in context: A036305 A370351 A257708 * A125827 A250191 A163654

Adjacent sequences: A266814 A266815 A266816 * A266818 A266819 A266820

KEYWORD

nonn,base

AUTHOR

Paolo P. Lava, Jan 04 2016

EXTENSIONS

a(19)-a(25) from Michael De Vlieger, Jan 12 2016

a(26) from Lars Blomberg, Feb 08 2016

Name corrected by and a(27)-a(35) from Giovanni Resta, Jun 06 2016

STATUS

approved