A093680 Sequence contains no 3-term arithmetic progression, starting with 1, 19.

1, 19, 20, 22, 23, 28, 29, 31, 32, 46, 47, 49, 50, 56, 58, 59, 82, 100, 101, 103, 104, 109, 110, 112, 113, 127, 128, 130, 131, 137, 139, 140, 244, 262, 263, 265, 266, 271, 272, 274, 275, 289, 290, 292, 293, 299, 301, 302, 325, 343, 344, 346, 347, 352, 353

Offset: 1

Author

Ralf Stephan, Apr 09 2004

Keywords

• nonn

Comments

a(1)=1, a(2)=19; a(n) is least k such that no three terms of a(1), a(2), ..., a(n-1), k form an arithmetic progression.

Links

• Index entries related to non-averaging sequences

Crossrefs

Cf. A004793, A033157, A093678, A093679, A093681, A092482.

Row 5 of array in A093682.

Formula

a(n) = (Sum_{k=1..n-1} (3^A007814(k) + 1)/2) + f(n), with f(n) a 16-periodic function with values {1, 18, 17, 18, 14, 18, 17, 19, 5, 18, 17, 18, 14, 19, 19, 19, ...}, as proved by Lawrence Sze.