OFFSET
0,2
COMMENTS
After a({1, 2, 3}), the next primes occur at indices 19, 20, 22, 25, 28, 30, 33, 36, 37, 39, 88, 279, 280, ... The prime a(88) = 20{248751}*8 (where {x}*n means x repeated n times) has 50 decimal digits, and the prime a(279) = 22487{512487}*31 has 191 digits, it is followed by the Fermat prime a(280) = 257 = A019434(4), which is the least positive integer not appearing earlier.
LINKS
Eric Angelini, Fun with roots, personal blog CinquanteSignes.blogspot.com (and post to the math-fun list), Jul 28 2024.
PROG
(PARI) upto(N=300, a=0, S=[])={vector(N, i, S=setunion(S, [a]); while(#S>1&&S[2]==S[1]+1, S=S[^1]); a=if(a%3 && !ispseudoprime(a), 10*a+(a-1)%9, S[1])+1)}
CROSSREFS
KEYWORD
nonn
AUTHOR
M. F. Hasler, Jul 30 2024
STATUS
approved