Let p be an odd prime number. Let S=a1,a2,… be the sequence defined as follows: a1=1,a2=2,…,ap−1=p−1, and for n≥p, an is the smallest integer greater than an−1 such that in a1,a2,…,an there are no arithmetic progressions of length p. We say that a positive integer is a ghost if it doesn’t appear in S.
What is the smallest ghost that is not a multiple of p?Proposed by Guerrero Mexiconumber theoryarithmetic sequenceinduction