%I #19 Nov 27 2024 15:44:38
%S 52,152,1052,1152,2152,2513,3152,4152,4316,5152,5201,5212,6152,6213,
%T 7152,8152,9152,10152,11052,11152,12152,12513,13152,14152,14316,15152,
%U 15201,15212,16152,16213,17152,18152,19152,20521,21052,21152,25103,25113,30251,30621,31052,31152,32519,41052,41152,43106
%N 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 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 Jean-Marc Falcoz, <a href="/A297627/b297627.txt">Table of n, a(n) for n = 1..7707</a>
%e 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 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 *)
%o (Python)
%o def ok(n):
%o s = str(n)
%o d = list(map(int, s))
%o sums = [d[i]**d[i+1] for i in range(len(s)-1)]
%o return sorted(s) == sorted("".join(str(t) for t in sums))
%o print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Nov 27 2024
%Y Cf. A296451, A296521.
%K base,nonn
%O 1,1
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Jan 02 2018