A379414 -id:A379414 - cp's OEIS frontend

A379415 a(n) = n + floor(nr/s) + floor(nt/s), where r = 3^(1/4), s = 3^(1/2), t = 3^(3/4).

2, 5, 8, 12, 14, 17, 21, 24, 26, 30, 33, 36, 39, 42, 45, 49, 51, 54, 58, 61, 63, 66, 70, 73, 75, 79, 82, 85, 89, 91, 94, 98, 101, 103, 107, 110, 113, 116, 119, 122, 125, 128, 131, 134, 138, 140, 143, 147, 150, 152, 156, 159, 162, 166, 168, 171, 175, 178, 180

Offset: 1

Clark Kimberling, Jan 18 2025

nonn

This sequence and A379414 and A379416 partition the positive integers; see A184812 for a proof.

Cf. A184812, A379415, A379416.

Cf. also A011002, A002194, A011022.

r = 3^(1/4); s = 3^(1/2); t = 3^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379414 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379415 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379416 *)

a(n) = n + floor(n/r) + floor(n*r), where r = 3^(1/4).

A379416 a(n) = n + [nr/t] + [ns/t], where r = 3^(1/4); s = 3^(1/2); t = 3^(3/4) and [ ] = floor.

Original entry on oeis.org

1, 4, 6, 9, 10, 13, 16, 18, 20, 22, 25, 27, 29, 32, 34, 37, 38, 41, 43, 46, 48, 50, 53, 55, 57, 60, 62, 65, 67, 69, 71, 74, 77, 78, 81, 83, 86, 87, 90, 93, 95, 97, 99, 102, 104, 106, 109, 111, 114, 115, 118, 121, 123, 126, 127, 130, 132, 135, 137, 139, 142

Offset: 1

Clark Kimberling, Jan 20 2025

nonn

This sequence and A379414 and A379415 partition the positive integers; see A184812 for a proof.

Cf. A184812, A379414, A379415.

r = 3^(1/4); s = 3^(1/2); t = 3^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379414 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379415 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379416 *)

a(n) = n + [n*r/t] + [n*s/t], where r = 3^(1/4); s = 3^(1/2); t = 3^(3/4) and [ ] = floor.

a(n) = n + [n/r] + [n/r^2], where r = 3^(1/4) and [ ] = floor.

cp's OEIS Frontend

A379415 a(n) = n + floor(nr/s) + floor(nt/s), where r = 3^(1/4), s = 3^(1/2), t = 3^(3/4).

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Formula

A379416 a(n) = n + [nr/t] + [ns/t], where r = 3^(1/4); s = 3^(1/2); t = 3^(3/4) and [ ] = floor.

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Formula

cp's OEIS Frontend

A379415 a(n) = n + floor(n*r/s) + floor(n*t/s), where r = 3^(1/4), s = 3^(1/2), t = 3^(3/4).

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

A379416 a(n) = n + [n*r/t] + [n*s/t], where r = 3^(1/4); s = 3^(1/2); t = 3^(3/4) and [ ] = floor.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Formula

A379415 a(n) = n + floor(nr/s) + floor(nt/s), where r = 3^(1/4), s = 3^(1/2), t = 3^(3/4).

A379416 a(n) = n + [nr/t] + [ns/t], where r = 3^(1/4); s = 3^(1/2); t = 3^(3/4) and [ ] = floor.