A100480 a(1)=1 and, for n>1, a(n) is the smallest positive integer such that the subset S(c) of {1,2,3,...,n} defined by S(c)={k|1<=k<=n; a(k)=c} does not contain a 3-term arithmetic progression for any integer c.

1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 5, 4, 4, 5, 1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 5, 4, 4, 5, 2, 3, 3, 4, 4, 5, 4, 4, 5, 5, 6, 6, 5, 6, 6, 7, 7, 8, 5, 6, 6, 5, 6, 6, 7, 7, 8, 1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 1, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 4, 4, 5

Offset

1,3

Comments

The sequence of values of n for which a(n)=1 is given by {A005836(i)-1}.

Links

Samuel B. Reid, Table of n, a(n) for n = 1..10000

Samuel B. Reid, Python program for A100480

Formula

a(n + 1) = A006997(n) + 1 for any n >= 0. - Rémy Sigrist, Jun 28 2022

Prog

(Python) # See Links section.

Crossrefs

Cf. A005836, A006997, A135415, A229037.

Sequence in context: A029333 A029261 A359384 * A373052 A268811 A371457

Adjacent sequences: A100477 A100478 A100479 * A100481 A100482 A100483

Keyword

nonn

Author

John W. Layman, Nov 22 2004

Status

approved