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A290788
Values of n such that 6^n ends in n, or expomorphic numbers in "base" 6.
3
6, 56, 656, 8656, 38656, 238656, 7238656, 47238656, 447238656, 7447238656, 27447238656, 227447238656, 3227447238656
OFFSET
1,1
COMMENTS
Definition: For positive integers b (as base) and n, the positive integer (allowing initial 0's) a(n) is expomorphic relative to base b (here 6) if a(n) has exactly n decimal digits and if b^a(n) == a(n) (mod 10^n) or, equivalently, b^a(n) ends in a(n). [See Crux Mathematicorum link.]
LINKS
Charles W. Trigg, Problem 559, Crux Mathematicorum, page 192, Vol. 7, Jun. 81.
EXAMPLE
6^6 = 46656 ends in 6, so 6 is a term.
6^56 = ...656 ends in 56, so 56 is another term.
MATHEMATICA
Select[Range[10^6], PowerMod[6, #, 10^(1 + Floor@ Log10[#])] == # &] (* Michael De Vlieger, Apr 13 2021 *)
PROG
(PARI) is(n)=my(m=10^#digits(n)); Mod(6, m)^n==n \\ Charles R Greathouse IV, Aug 10 2017
CROSSREFS
Cf. A064541 (base 2), A183613 (base 3), A288845 (base 4), A289138, A306570 (base 5), A306686 (base 9).
Cf. A003226 (automorphic numbers), A033819 (trimorphic numbers).
Sequence in context: A285166 A182955 A053336 * A215507 A112699 A093197
KEYWORD
nonn,base,more
AUTHOR
Bernard Schott, Aug 10 2017
EXTENSIONS
a(6)-a(9) from Charles R Greathouse IV, Aug 10 2017
a(10)-a(13) from Chai Wah Wu, Apr 13 2021
STATUS
approved