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 1-3 of 3 results.

A329017 a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.

Original entry on oeis.org

1, 1, 7, 13, 11, 133, 463, 1261, 4039, 2321, 35839, 105469, 320503, 953317, 575267, 8596237, 25854247, 77431669, 232557151, 139429433, 2092490071, 6275373061, 18830313487, 56482551853, 6778577311, 508359743893, 1525146340543, 4575304803901, 13726182847159
Offset: 1

Views

Author

Clark Kimberling, Nov 23 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 A328644.

Crossrefs

Cf. A328644, A329018, A329019.

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[3/2]; 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}]];  (* A328644 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329017 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329018 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329019 *)
(* Peter J. C. Moses, Nov 01 2019 *)

A329018 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.

Original entry on oeis.org

1, 7, 43, 259, 311, 9331, 55987, 335923, 2015539, 2418647, 72559411, 435356467, 2612138803, 15672832819, 18807399383, 564221981491, 3385331888947, 20311991333683, 121871948002099, 146246337602519, 4387390128075571, 26324340768453427, 157946044610720563
Offset: 1

Views

Author

Clark Kimberling, Nov 23 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 A328644.

Crossrefs

Cf. A328644, A329017, A329019.

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[3/2]; 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}]];  (* A328644 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329017 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329018 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329019 *)
(* Peter J. C. Moses, Nov 01 2019 *)

A329019 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.

Original entry on oeis.org

1, 13, 133, 1261, 2321, 105469, 953317, 8596237, 77431669, 139429433, 6275373061, 56482551853, 508359743893, 4575304803901, 8235602334113, 370603178776909, 3335432903959477, 30018913315504477, 270170288559017029, 486306574381812041, 21883796946693169621
Offset: 1

Views

Author

Clark Kimberling, Nov 23 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 A328644.

Crossrefs

Cf. A328644, A329017, A329018.

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[3/2]; 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}]];  (* A328644 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329017 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329018 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329019 *)
(* Peter J. C. Moses, Nov 01 2019 *)
Showing 1-3 of 3 results.

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