A227071 Let s(m) = the set of k > 0 such that k^m ends with k. Then a(n) = least m such that s(m) = s(n).

1, 2, 3, 2, 5, 6, 3, 2, 9, 2, 11, 2, 5, 2, 3, 6, 17, 2, 3, 2, 21, 2, 3, 2, 9, 26, 3, 2, 5, 2, 11, 2, 33, 2, 3, 6, 5, 2, 3, 2, 41, 2, 3, 2, 5, 6, 3, 2, 17, 2, 51, 2, 5, 2, 3, 6, 9, 2, 3, 2, 21, 2, 3, 2, 65, 6, 3, 2, 5, 2, 11, 2, 9, 2, 3, 26, 5, 2, 3, 2, 81, 2

Offset: 1

Author

T. D. Noe, Jul 29 2013

Keywords

• nonn
• base

Comments

See A227070 for more details and for the numbers n such that n = a(n).

The entries in the b-file have been tentatively obtained by comparing the terms < 10^30 in the sets s(n). - Giovanni Resta, Jul 30 2013

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (warning: contains tentative terms)

Crossrefs

Cf. A003226 (n=2), A033819 (n=3), A068407 (n=5), A068408 (n=6).

Cf. A072496 (n=11), A072495 (n=21), A076650 (n=26).

Cf. A227070 (n such that n = a(n)).

Programs

Mathematica

ts = {{}}; t2 = {1}; te = {1}; Do[s = Select[Range[0, 10^7], PowerMod[#, n, 10^IntegerLength[#]] == # &]; If[MemberQ[ts, s], AppendTo[t2, te[[Position[ts, s, 1, 1][[1, 1]]]]], AppendTo[ts, s]; AppendTo[te, n]; AppendTo[t2, n]], {n, 2, 82}]; t2

Formula

Conjecture: a(n+1) = A132741(n) + 1. - Eric M. Schmidt, Jul 30 2013

Extensions

Mathematica program and some entries corrected by Giovanni Resta, Jul 30 2013