A351410 Numbers m such that the decimal representation of 8^m ends in m.

56, 856, 5856, 25856, 225856, 5225856, 95225856, 895225856, 6895225856, 16895225856, 416895225856, 5416895225856, 35416895225856, 7035416895225856, 77035416895225856, 577035416895225856, 1577035416895225856, 21577035416895225856, 521577035416895225856, 1521577035416895225856, 81521577035416895225856

Offset: 1

Author

Bernard Schott, Feb 10 2022

Keywords

• nonn
• base

Comments

The Crux Mathematicorum link calls these numbers "expomorphic" relative to "base" b, with here b = 8.

Under that definition, the term after a(13) = 35416895225856 is not "035416895225856" or "35416895225856" but a(14) = 7035416895225856.

Conjecture: if k(n) is "expomorphic" relative to "base" b, then the next one in the sequence, k(n+1), consists of the last n+1 digits of b^k(n).

This conjecture is true. See A133618. - David A. Corneth, Feb 10 2022

Examples

			8^56 = 374144419156711147060143317175368453031918731001856, so 56 is a term.
8^856 = ...5856 ends in 856, so 856 is another term.
		

Links

• Charles W. Trigg, Problem 559, Crux Mathematicorum, pp. 192-194, Vol. 7, Jun. 1981.

Crossrefs

Cf. A064541, A183613, A288845, A306570, A290788, A321970, this sequence, A306686, A289138.

Cf. A003226 (automorphic numbers), A033819 (trimorphic numbers).

Cf. A133618 (leading digits).

Extensions

a(7)-a(8) from Michel Marcus, Feb 10 2022

More terms from David A. Corneth, Feb 10 2022