A329012 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(5) as in A327322.

1, 7, 52, 406, 16496, 27664, 1663936, 2081968, 18513664, 833245952, 16665967616, 13888655872, 1666655481856, 8333310963712, 55555495903232, 104166621927424, 16666663803355136, 9259258622967808, 1666666620853682176, 4166666620853682176, 55555555311219638272

Offset

1,2

Comments

a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)). Conjecture: there is no upper bound for the number of consecutive equal digits among numbers in this sequence, as suggested, for example, by 34 straight 1's in a(96) and 38 straight 6's in a(97).

Links

Table of n, a(n) for n=1..21.

Example

See Example in A327322.

Mathematica

c[poly_] := If[Head[poly] === Times, Times @@ DeleteCases[(#1 (Boole[MemberQ[#1, x] || MemberQ[#1, y] || MemberQ[#1, z]] &) /@Variables /@ #1 &)[List @@ poly], 0], poly];
r = Sqrt[5]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];
Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]];  (* A327322 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329011 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329012 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329013 *)
(* Peter J. C. Moses, Nov 01 2019 *)

Crossrefs

Cf. A327320, A327321, A329011, A329013.

Sequence in context: A259554 A370027 A147962 * A349532 A369147 A162233

Adjacent sequences: A329009 A329010 A329011 * A329013 A329014 A329015

Keyword

nonn,easy

Author

Clark Kimberling, Nov 23 2019

Status

approved