

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

JeanMarc Falcoz, Table of n, a(n) for n = 1..7707


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

Cf. A296451, A296521.
Sequence in context: A227703 A044384 A044765 * A049059 A292172 A166390
Adjacent sequences: A297624 A297625 A297626 * A297628 A297629 A297630


KEYWORD

base,nonn


AUTHOR

Eric Angelini and JeanMarc Falcoz, Jan 02 2018


STATUS

approved



