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

1,2

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

Table of n, a(n) for n=1..55.

Index entries related to non-averaging sequences

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.

Crossrefs

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

Row 5 of array in A093682.

Sequence in context: A004508 A018824 A289469 * A007640 A265201 A274340

Adjacent sequences: A093677 A093678 A093679 * A093681 A093682 A093683

Keyword

nonn

Author

Ralf Stephan, Apr 09 2004

Status

approved