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.

A329014 a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.

Original entry on oeis.org

1, 5, 31, 185, 1111, 6665, 5713, 239945, 1439671, 8638025, 51828151, 310968905, 1865813431, 1599268655, 67169283511, 403015701065, 2418094206391, 14508565238345, 87051391430071, 522308348580425, 447692870211793, 18803100548895305, 112818603293371831
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 A327323.

Crossrefs

Cf. A327323, A329015, A329016.

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[6]; 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}]];  (* A327323 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329014 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329015 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329016 *)
(* Peter J. C. Moses, Nov 01 2019 *)

A329015 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.

Original entry on oeis.org

1, 17, 229, 2873, 35101, 424337, 729667, 61370153, 736832461, 8843942657, 106137077509, 1273693758233, 15284569239421, 26202293082311, 2200998722429749, 26412015186735113, 316944334828711981, 3803332780883996897, 45639997185305228389, 547679985297149068793
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 A327323.

Crossrefs

Cf. A327323, A329014, A329016.

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[6]; 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}]];  (* A327323 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329014 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329015 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329016 *)
(* Peter J. C. Moses, Nov 01 2019 *)

A329016 a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.

Original entry on oeis.org

1, 29, 643, 12905, 246931, 4605809, 12096589, 1543657385, 28000191811, 506361400289, 9140442629803, 164813279007065, 2969777450503891, 7641502403030567, 963209052615434683, 17341940195247239945, 312200873244313891171, 5620121165426149334849
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 A327323.

Crossrefs

Cf. A327323, A329014, A329015.

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[6]; 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}]];  (* A327323 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329014 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329015 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329016 *)
(* Peter J. C. Moses, Nov 01 2019 *)
Showing 1-3 of 3 results.

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