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.

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A379409 a(n) = n + floor(n*r/s) + floor(n*t/s), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).

Original entry on oeis.org

2, 5, 8, 11, 14, 17, 20, 24, 26, 29, 32, 35, 38, 41, 44, 48, 51, 53, 56, 59, 62, 65, 68, 72, 75, 78, 80, 83, 86, 89, 92, 96, 99, 102, 105, 107, 110, 113, 116, 120, 123, 126, 129, 132, 134, 137, 141, 144, 147, 150, 153, 156, 158, 161, 165, 168, 171, 174, 177
Offset: 1

Views

Author

Clark Kimberling, Jan 15 2025

Keywords

Comments

This sequence and A379408 and A379410 partition the positive integers.

Crossrefs

Cf. A001622, A379408, A379410.

Programs

  • Mathematica
    u = (1 + 5^(1/2))/2;
r = u^(1/4); s = u^(1/2); t = u^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379408 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379409 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379410 *)

Formula

a(n) = n + floor(n/r) + floor(n*r), where r = u^(1/4), u = golden ratio.

A379410 a(n) = n + floor(n*r/t) + floor(n*s/t), where r = u^(1/4), s = u^(1/2), t = u^(3/4), u = golden ratio (A001622).

Original entry on oeis.org

1, 4, 7, 10, 12, 15, 18, 21, 23, 25, 28, 31, 34, 37, 39, 42, 45, 47, 49, 52, 55, 58, 61, 63, 66, 69, 71, 74, 76, 79, 82, 85, 87, 90, 93, 95, 98, 100, 103, 106, 109, 112, 114, 117, 119, 122, 124, 127, 130, 133, 136, 138, 140, 143, 146, 149, 151, 154, 157, 160, 162, 164, 167, 170
Offset: 1

Views

Author

Clark Kimberling, Jan 21 2025

Keywords

Comments

This sequence, A379408, and A379409 partition the positive integers.

Crossrefs

Cf. A001622, A184908, A379408, A379409.

Programs

  • Mathematica
    u = (1 + 5^(1/2))/2;
r = u^(1/4); s = u^(1/2); t = u^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379408 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379409 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379410 *)

Formula

a(n) = n + floor(n/r^2) + floor(n/r), where r = u^(1/4), u = golden ratio.

Extensions

Values corrected by R. J. Mathar, Jan 28 2025
Showing 1-2 of 2 results.

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

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