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

Author

John W. Layman, Nov 22 2004

Keywords

• nonn

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

Crossrefs

Cf. A005836, A006997, A135415, A229037.

Programs

Python

# See Links section.

Formula

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