A100480 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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.