

A098174


a(n) is the smallest e > 0 such that the initial digit of n^e = 1 in decimal representation.


3



1, 4, 9, 2, 3, 4, 5, 8, 16, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 4, 3, 3, 3, 3, 3, 3, 5, 7, 9, 25, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 5, 11, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 13, 14, 16, 18, 20, 23, 27, 32, 40, 53
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OFFSET

1,2


COMMENTS

A000030(n^a(n)) = 1; A098175(n) = n^a(n).
From Rémy Sigrist, Jun 25 2018: (Start)
We can extend this sequence to every Gaussian integers as follows:
 for any Gaussian integer z, let f(z) be the least k > 0 such that the initial decimal digit of the real part of z^k equals 1, or 1 if no such k exists,
 naturally f(n) = a(n) for any n > 0,
 apparently f(z) = 1 iff z = 0,
 see Links section for the color plot of f.
(End)


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Color plot of f(x + i*y) for x = 200..1000 and y = 200..500


PROG

(PARI) a(n, base=10) = my (nk=n); for (k=1, oo, my (z); logint(nk, base, &z); if (nk\z==1, return (k), nk*=n)) \\ Rémy Sigrist, Jun 21 2018


CROSSREFS

Cf. A000030, A098175, A131835.
Sequence in context: A238592 A229553 A254061 * A126709 A254159 A125575
Adjacent sequences: A098171 A098172 A098173 * A098175 A098176 A098177


KEYWORD

nonn,base


AUTHOR

Reinhard Zumkeller, Aug 30 2004


STATUS

approved



