A119753 - OEIS

%I #3 Mar 30 2012 18:36:04

%S 3,5,7,11,13,19,71,73,79,139,431,433,439,499,859,4091,4093,4099,4159,

%T 4519,8179,86531,86533,86539,86599,86959,90619,173059,513101,513103,

%U 513109,513169,513529,517189,599629,1026199,913571,913573,913579,913639

%N Prime numbers in their order of occurrence and generated by A119751, the sequence of odd numbers defined recursively by a(1)=1 and a(i) + a(j) + 1 is prime for all i,j.

%F Let a(n) be the sequence defined recursively by a(1)=1 and a(n) is the first odd number greater than a(n-1) such that 2*a(n)+1 is prime and a(i) + a(n) + 1 is prime for all i<=n-1. Then p(n) is the n-th prime in the lexicographic order a(i) + a(j) + 1, i>=j.

%e a(1)=1, a(2)=3 so 1+1+1=3, 1+3+1=5, 3+3+1=7 so the first three elements are 3, 5, 7.

%p OP:=[1]: P:=[3]: for w to 1 do for n from 0 to 12^6 do s:=6*n+3; Q:=map(z->s+z+1,[op(OP),s]); if andmap(isprime,Q) then OP:=[op(OP),s]; P:=[op(P),op(Q)]; print(s); print(Q); fi; od od; OP; P;

%K nonn

%O 1,1

%A _Walter Kehowski_, Jun 17 2006, Jun 19 2006, Jun 25 2006