A379417 a(n) = n + [n*s/r] + [n*t/r], where r = (3/2)^(1/4); s = (3/2)^(1/2); t = (3/2)^(3/4) and [ ] = floor.

3, 6, 9, 12, 16, 19, 22, 25, 29, 33, 36, 39, 42, 46, 49, 52, 55, 59, 63, 66, 69, 72, 76, 79, 82, 85, 89, 92, 96, 99, 102, 106, 109, 112, 115, 119, 122, 126, 129, 132, 136, 139, 142, 145, 149, 152, 156, 159, 163, 166, 169, 172, 175, 179, 182, 185, 189, 193

Offset

1,1

Comments

This sequence and A379418 and A379419 partition the positive integers; see A184812 for a proof. For each k in A000027, write "a" if k=A379417(n) for some n, "b" if k=A379418(n) for some n, and "c" if k=A379419(n) for some n. Concatenating these letters for k = 1,2,3,... spells the following infinite word:

cbacbacbacbacbcabcabcabcabccabcbacbacbacbacbcabcabcabcacbcabcbacbacbacbacbcabcabcabcacbcabcabcbacbacbacbcabcabcacbacbcabcabcbacbacbacbcabcacbacbacbcabcabcbacbacbcab...

Links

Table of n, a(n) for n=1..58.

Formula

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

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

Mathematica

r = (3/2)^(1/4); s = (3/2)^(1/2); t = (3/2)^(3/4);
Table[n + Floor[n*s/r] + Floor[n*t/r], {n, 1, 120}]  (* A379417 *)
Table[n + Floor[n*r/s] + Floor[n*t/s], {n, 1, 120}]  (* A379418 *)
Table[n + Floor[n*r/t] + Floor[n*s/t], {n, 1, 120}]  (* A379419 *)

Crossrefs

Cf. A184812, A379418, A379419.

Sequence in context: A194146 A276854 A184906 * A186156 A211267 A084515

Adjacent sequences: A379414 A379415 A379416 * A379418 A379419 A379420

Keyword

nonn

Author

Clark Kimberling, Jan 20 2025

Status

approved