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A266817 Numbers x = concat(a,b) such that b^a begins with the digits of x. 3
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 (list; graph; refs; listen; history; text; internal format)
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: A338009 A036305 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

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Last modified July 1 12:12 EDT 2022. Contains 354972 sequences. (Running on oeis4.)