A054869 Digits of an idempotent 6-adic number.

3, 1, 2, 0, 5, 3, 1, 2, 2, 2, 5, 1, 5, 5, 1, 4, 1, 3, 1, 2, 5, 5, 5, 0, 5, 2, 5, 5, 5, 3, 1, 4, 3, 3, 0, 4, 2, 2, 4, 0, 1, 3, 3, 1, 4, 0, 2, 0, 1, 2, 5, 2, 4, 0, 2, 3, 3, 0, 3, 4, 5, 5, 2, 5, 5, 4, 3, 2, 3, 1, 5, 4, 5, 4, 0, 1, 1, 0, 4, 2, 0, 1, 3, 0, 1, 5, 0, 4, 3, 5, 0, 1, 0, 2, 4, 0, 3, 4, 2

Offset

0,1

Comments

( a(0) + a(1)*6 + a(2)*6^2 + ... )^k = a(0) + a(1)*6 + a(2)*6^2 + ... for each k. Apart from 0 and 1, in base 6 there are only 2 numbers with this property. For the other see A055620.

References

V. deGuerre and R. A. Fairbairn, Automorphic numbers, J. Rec. Math., 1 (No. 3, 1968), 173-179.

Links

Kenny Lau, Table of n, a(n) for n = 0..9999

V. deGuerre and R. A. Fairbairn, Automorphic numbers, Jnl. Rec. Math., 1 (No. 3, 1968), 173-179

Formula

a(n) == 3^(2^n) (mod 6^n). - Robert Dawson, Oct 28 2022

Prog

(Python)
n=10000; res=1-pow((3**n+1)//2, n, 3**n)*2**n
for i in range(n):print(i, res%6); res//=6
# Kenny Lau, Jun 09 2018

Crossrefs

The six examples given by deGuerre and Fairbairn are A055620, A054869, A018247, A018248, A259468, A259469.

Sequence in context: A265910 A222212 A318526 * A201671 A226590 A261349

Adjacent sequences: A054866 A054867 A054868 * A054870 A054871 A054872

Keyword

nonn,base

Author

Paolo Dominici (pl.dm(AT)libero.it), May 23 2000

Status

approved