cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-2 of 2 results.

A329005 a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.

Original entry on oeis.org

1, 1, 1, 5, 11, 7, 43, 85, 19, 341, 683, 455, 2731, 5461, 3641, 21845, 43691, 9709, 174763, 349525, 233017, 1398101, 2796203, 1864135, 11184811, 22369621, 1657009, 89478485, 178956971, 119304647, 715827883, 1431655765, 954437177, 5726623061, 11453246123
Offset: 1

Views

Author

Clark Kimberling, Nov 08 2019

Keywords

Comments

a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).

Examples

			See Example in A327320.

Crossrefs

Cf. A327320, A329006, A329007.

Programs

  • 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[2]; 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}]];  (* A327320 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329005 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329006 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329007 *)
(* Peter J. C. Moses, Nov 01 2019 *)

A329007 a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.

Original entry on oeis.org

1, 9, 21, 405, 2511, 5103, 92583, 557685, 372519, 20135709, 120873303, 241805655, 4353033231, 26119793709, 52241181741, 940355620245, 5642176768191, 3761465527701, 203119525916343, 1218718317759525, 2437437797780517, 43873890820402509, 263243376303474663
Offset: 1

Views

Author

Clark Kimberling, Nov 08 2019

Keywords

Comments

a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).

Examples

			See Example in A327320.

Crossrefs

Cf. A327320, A329005, A329006.

Programs

  • 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[2]; 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}]];  (* A327320 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329005 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329006 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329007 *)
(* Peter J. C. Moses, Nov 01 2019 *)
Showing 1-2 of 2 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.