A098174 - OEIS

A098174

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

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

(list; graph; refs; listen; history; text; internal format)

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 A125575 A254159

Adjacent sequences: A098171 A098172 A098173 * A098175 A098176 A098177

KEYWORD

nonn,base

AUTHOR

Reinhard Zumkeller, Aug 30 2004

STATUS

approved