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A212155 Digits of one of the three 7-adic integers (-1)^(1/3). 7
5, 2, 0, 3, 6, 4, 0, 4, 2, 3, 2, 2, 1, 4, 5, 4, 5, 2, 0, 5, 5, 3, 1, 6, 4, 3, 2, 5, 3, 2, 3, 1, 0, 0, 4, 4, 4, 6, 4, 2, 6, 0, 0, 5, 1, 2, 5, 4, 3, 2, 5, 3, 2, 6, 3, 3, 4, 2, 2, 2, 1, 5, 6, 2, 6, 4, 6, 3, 5, 6, 4, 0, 5, 1, 4, 1, 1, 0, 6, 0, 4, 2, 2, 4, 5, 0, 3, 2, 1, 1, 5, 6, 2, 4, 2, 2, 1, 1, 5, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A210853 for comments and an approximation to this 7-adic number, called there v.  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):=A212153(n) and c(n):=A212154(n). a(0) = 5, one of the three solutions of X^3+1 == 0 (mod 7).

Since b(n) == 5 (mod 7), a(n) == 4 * c(n) (mod 7) for n>0. - Álvar Ibeas, Feb 20 2017

LINKS

Table of n, a(n) for n=0..99.

FORMULA

a(n) = (b(n+1) - b(n))/7^n, n>=1, with b(n):=A212153(n), defined by a recurrence given there. One also finds there a Maple program for b(n). a(0)=5.

a(n) = 6 - A212152(n), for n>0. - Álvar Ibeas, Feb 21 2017

CROSSREFS

Cf. A210850, A210851  (the p=5 case),  A212152, 6*A000012 (only entries 6).

Sequence in context: A334708 A201528 A093814 * A269328 A063377 A296493

Adjacent sequences:  A212152 A212153 A212154 * A212156 A212157 A212158

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, May 02 2012

STATUS

approved

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Last modified July 8 19:20 EDT 2020. Contains 335524 sequences. (Running on oeis4.)