login
A351410
Numbers m such that the decimal representation of 8^m ends in m.
0
56, 856, 5856, 25856, 225856, 5225856, 95225856, 895225856, 6895225856, 16895225856, 416895225856, 5416895225856, 35416895225856, 7035416895225856, 77035416895225856, 577035416895225856, 1577035416895225856, 21577035416895225856, 521577035416895225856, 1521577035416895225856, 81521577035416895225856
OFFSET
1,1
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
LINKS
Charles W. Trigg, Problem 559, Crux Mathematicorum, pp. 192-194, Vol. 7, Jun. 1981.
EXAMPLE
8^56 = 374144419156711147060143317175368453031918731001856, so 56 is a term.
8^856 = ...5856 ends in 856, so 856 is another term.
CROSSREFS
Cf. A003226 (automorphic numbers), A033819 (trimorphic numbers).
Cf. A133618 (leading digits).
Sequence in context: A182866 A008389 A338002 * A219937 A008921 A252181
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Feb 10 2022
EXTENSIONS
a(7)-a(8) from Michel Marcus, Feb 10 2022
More terms from David A. Corneth, Feb 10 2022
STATUS
approved