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

1, 18, 140, 20, 479393, 219600095, 4804461081, 686351583, 6679631931865, 82080661415031, 8898622841908566, 174149720118385232, 7290250572352382182, 65315972853762054047, 98713213404986046050649, 11532114009920222592500432, 356054521382275298405890644, 28999349909865958163356878647

Offset: 0

Author

Wolfdieter Lang, May 02 2012

Keywords

• nonn
• easy

Comments

a(n) is an 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.

Examples

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

Links

• Paolo Xausa, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A210848, A210849 (the p=5 case), A210853, A212153, A212156.

Programs

Mathematica

Join[{1}, MapIndexed[(#^3 + 1)/7^#2[[1]] &, FoldList[PowerMod[#, 7, 7^#2] &, 5, Range[2, 20]]]] (* Paolo Xausa, Jan 14 2025 *)

Formula

a(n) = (A212153(n)^3 + 1)/7^n.