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%I A297627 #15 Jan 31 2018 06:44:30
%S A297627 52,152,1052,1152,2152,2513,3152,4152,4316,5152,5201,5212,6152,6213,
%T A297627 7152,8152,9152,10152,11052,11152,12152,12513,13152,14152,14316,15152,
%U A297627 15201,15212,16152,16213,17152,18152,19152,20521,21052,21152,25103,25113,30251,30621,31052,31152,32519,41052,41152,43106
%N A297627 Anagrexpo integers: integers N that exactly reproduce their set of digits when we form the set of exponentiation of pairs of adjacent digits, from left to right.
%C A297627 The sequence is infinite, since any term of the sequence can be preceded by as many 1s as needed. The name "anagrexpo integers" comes from "anagram by exponentiation". The same idea is explored by the "anagraprod integers" and the "anagrasum integers" (see "Crossrefs" section hereunder).
%H A297627 Jean-Marc Falcoz, <a href="/A297627/b297627.txt">Table of n, a(n) for n = 1..7707</a>
%e A297627 a(2) = 152 reproduces the digits 1, 5 and 2 (in a different order) when the exponentiations 1^5=1 and 5^2=25 are taken. The same with a(6) = 2513, which reproduces the digits 2, 5, 1, and 3 when the exponentiations 2^5=32, 5^1=5 and 1^3=1 are taken.
%t A297627 Unprotect[Power]; Power[0, 0] := 1; Protect[Power]; Select[Range[10^5], SameQ @@ {Sort@ Flatten@ Map[IntegerDigits[Power @@ #] &, Partition[#, 2, 1]], Sort@ #} &@ IntegerDigits@ # &] (* _Michael De Vlieger_, Jan 02 2018 *)
%Y A297627 Cf. A296451, A296521.
%K A297627 base,nonn
%O A297627 1,1
%A A297627 _Eric Angelini_ and _Jean-Marc Falcoz_, Jan 02 2018

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