%I #53 Feb 11 2022 09:36:02
%S 56,856,5856,25856,225856,5225856,95225856,895225856,6895225856,
%T 16895225856,416895225856,5416895225856,35416895225856,
%U 7035416895225856,77035416895225856,577035416895225856,1577035416895225856,21577035416895225856,521577035416895225856,1521577035416895225856,81521577035416895225856
%N Numbers m such that the decimal representation of 8^m ends in m.
%C The Crux Mathematicorum link calls these numbers "expomorphic" relative to "base" b, with here b = 8.
%C Under that definition, the term after a(13) = 35416895225856 is not "035416895225856" or "35416895225856" but a(14) = 7035416895225856.
%C 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).
%C This conjecture is true. See A133618. - _David A. Corneth_, Feb 10 2022
%H Charles W. Trigg, <a href="https://cms.math.ca/wp-content/uploads/crux-pdfs/Crux_v7n06_Jun.pdf">Problem 559</a>, Crux Mathematicorum, pp. 192-194, Vol. 7, Jun. 1981.
%e 8^56 = 374144419156711147060143317175368453031918731001856, so 56 is a term.
%e 8^856 = ...5856 ends in 856, so 856 is another term.
%Y Cf. A064541, A183613, A288845, A306570, A290788, A321970, this sequence, A306686, A289138.
%Y Cf. A003226 (automorphic numbers), A033819 (trimorphic numbers).
%Y Cf. A133618 (leading digits).
%K nonn,base
%O 1,1
%A _Bernard Schott_, Feb 10 2022
%E a(7)-a(8) from _Michel Marcus_, Feb 10 2022
%E More terms from _David A. Corneth_, Feb 10 2022