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.

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

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

Jean-Marc 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 A345240 A292172

Adjacent sequences: A297624 A297625 A297626 * A297628 A297629 A297630

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Jan 02 2018

Status

approved