A379409 -id:A379409 - cp's OEIS frontend

A379408 a(n) = n + floor(ns/r) + floor(nt/r), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).

3, 6, 9, 13, 16, 19, 22, 27, 30, 33, 36, 40, 43, 46, 50, 54, 57, 60, 64, 67, 70, 73, 77, 81, 84, 88, 91, 94, 97, 101, 104, 108, 111, 115, 118, 121, 125, 128, 131, 135, 139, 142, 145, 148, 152, 155, 159, 163, 166, 169, 172, 176, 179, 182, 186, 190, 193, 196

Offset: 1

Clark Kimberling, Jan 15 2025

nonn

This sequence and A379409 and A379410 partition the positive integers. For each k in A000027, write "a" if k=A379408(n) for some n, "b" if k=A379409(n) for some n, and "c" if k=A379410(n) for some n. Concatenating these letters for k = 1,2,3,... spells the following infinite word:

cbacbacbacbcabcabcabcacbcbacbacbacbacbcabcabcacbcabcbacbacbacbcabcabcacbacbcabcbacbacbcabcabcacbacbcabcabcb...

Cf. A000027, A001622, A379409, A379410.

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 *)

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

A379410 a(n) = n + floor(nr/t) + floor(ns/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

Clark Kimberling, Jan 21 2025

nonn

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

Cf. A001622, A184908, A379408, A379409.

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 *)

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

Values corrected by R. J. Mathar, Jan 28 2025

cp's OEIS Frontend

A379408 a(n) = n + floor(ns/r) + floor(nt/r), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).

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

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cp's OEIS Frontend

A379408 a(n) = n + floor(n*s/r) + floor(n*t/r), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

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).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

Extensions

A379408 a(n) = n + floor(ns/r) + floor(nt/r), where r = u^(1/4); s = u^(1/2); t = u^(3/4), u = golden ratio (A001622).

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