login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A329012 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(5) as in A327322. 3
1, 7, 52, 406, 16496, 27664, 1663936, 2081968, 18513664, 833245952, 16665967616, 13888655872, 1666655481856, 8333310963712, 55555495903232, 104166621927424, 16666663803355136, 9259258622967808, 1666666620853682176, 4166666620853682176, 55555555311219638272 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A259554 A370027 A147962 * A349532 A369147 A162233
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 23 2019
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 10:31 EDT 2024. Contains 371240 sequences. (Running on oeis4.)