OFFSET
0,1
COMMENTS
See A210852 for comments and an approximation to this 7-adic number, called there u. See also A048898 for references on p-adic numbers.
a(n), n>=1, is the (unique) solution of the linear congruence 3 * b(n)^2 * a(n) + c(n) == 0 (mod 7), with b(n):=A210852(n) and c(n):=A210853(n). a(0) = 3, one of the three solutions of x^3+1 == 0 (mod 7).
Since b(n) == 3 (mod 7), a(n) == c(n) (mod 7) for n>0. - Álvar Ibeas, Feb 20 2017
With a(0) = 2, this is the digits of one of the three cube root of 1, the one that is congruent to 2 modulo 7. - Jianing Song, Aug 26 2022
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
a(n) = (b(n+1) - b(n))/7^n, n>=1, with b(n):=A210852(n), defined by a recurrence given there. One also finds a Maple program for b(n) there. a(0)=3.
MAPLE
op([1, 1, 3], select(t -> padic:-ratvaluep(t, 1)=3, [padic:-rootp(x^3+1, 7, 100)])); # Robert Israel, Mar 27 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, May 02 2012
STATUS
approved