

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.


1



52, 152, 1052, 1152, 2152, 2513, 3152, 4152, 4316, 5152, 5201, 5212, 6152, 6213, 7152, 8152, 9152, 10152, 11052, 11152, 12152, 12513, 13152, 14152, 14316, 15152, 15201, 15212, 16152, 16213, 17152, 18152, 19152, 20521, 21052, 21152, 25103, 25113, 30251, 30621, 31052, 31152, 32519, 41052, 41152, 43106
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OFFSET

1,1


COMMENTS

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).


LINKS



EXAMPLE

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.


MATHEMATICA

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 *)


CROSSREFS



KEYWORD

base,nonn


AUTHOR



STATUS

approved



