A212154 (A212153(n)^3 + 1)/7^n, n >= 0.

1, 18, 140, 20, 479393, 219600095, 4804461081, 686351583, 6679631931865, 82080661415031, 8898622841908566, 174149720118385232, 7290250572352382182, 65315972853762054047, 98713213404986046050649

Offset

0,2

Comments

a(n) is integer because A212153(n) is one of the three solutions of X(n)^3+1 == 0 (mod 7^n), namely the one satisfying also X(n) == 5 (mod 7).

See the comments on A210853, 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):=A212153(n) given by a recurrence. See also a Maple program for b(n) there.

Example

a(0) = 1/1 = 1.
a(3) = (19^3 + 1)/7^3 = 6860/343  = 20, (b(3) = 19^7 (mod 7^3) = 19).

Crossrefs

Cf. A210848, A210849 (the p=5 case). A210853, A212156.

Sequence in context: A114239 A087115 A163707 * A108680 A204273 A081074

Adjacent sequences: A212151 A212152 A212153 * A212155 A212156 A212157

Keyword

nonn,easy

Author

Wolfdieter Lang, May 02 2012

Status

approved