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A212156 ((6*A023000(n))^3 + 1)/7^n, n >= 0. 2
1, 31, 2257, 116623, 5757601, 282424831, 13840934257, 678220602223, 33232913275201, 1628413476849631, 79792265450186257, 3909821042651007823, 191581231339042552801, 9387480337357087274431, 459986536542705291758257 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is integer because 6*A023000(n) is one of three solution of X(n)^3+1 == 0 (mod 7^n), namely the one satisfying also X(n) == 6 (mod 7) == -1 (mod 7).

See the comments on A210852, and the Nagell reference given in A210848.

LINKS

Table of n, a(n) for n=0..14.

FORMULA

a(n) = (b(n)^3+1)/7^n, n>=0, with b(n):=6*A023000(n) given by a recurrence obtained from the one of A023000. There also programs for b(n)/6 are given.

EXAMPLE

a(0) = 1/1 = 1.

a(3) = ((6*57)^3 + 1)/7^3 = 40001689/343  = 116623,  (b(3) = 48^7 (mod 7^3) = 342 = 6*57).

CROSSREFS

Cf.  A210848, A210849 (the p=5 case). A210853, A212154.

Sequence in context: A218352 A297549 A292706 * A297806 A219076 A072019

Adjacent sequences:  A212153 A212154 A212155 * A212157 A212158 A212159

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, May 02 2012

STATUS

approved

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Last modified August 7 23:38 EDT 2020. Contains 336279 sequences. (Running on oeis4.)