The submissions stack has been unacceptably high for several months now. Please voluntarily restrict your submissions and please help with the editing. (We don't want to have to impose further limits.)
A138683
a(1)=1 and, for n>1, a(n) is the smallest integer greater than a(n-1) such that a(n) and a(k) do not sum to a term of A001333 (Numerators of continued fraction convergents to sqrt(2)).