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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
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
Sequence in context: A036305 A370351 A257708 * A125827 A250191 A163654
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 February 22 08:27 EST 2024. Contains 370240 sequences. (Running on oeis4.)