OFFSET
1,1
COMMENTS
The primes are p(i) + p(j) + 1, j<=i, are not distinct for the (i,j) pairs (2,2),(3,1), with prime=17 and (6,6),(7,1), with prime=1277.
FORMULA
Let a(n) be the sequence defined recursively by a(1)=2 and a(n) is the first even 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.
EXAMPLE
a(1)=2, a(2)=8 so 2+2+1=5, 8+2+1=11, 8+8+1=17 so the first three elements are 5, 11, 17.
MAPLE
EP:=[]: P:=[]: for w to 1 do for n from 0 to 12^6 do s:=6*n+2; Q:=map(z->s+z+1, [op(EP), s]); if andmap(isprime, Q) then EP:=[op(EP), s]; P:=[op(P), op(Q)]; print(s); print(Q); fi; od od; EP; P;
CROSSREFS
KEYWORD
nonn
AUTHOR
Walter Kehowski, Jun 17 2006, Jun 19 2006, Jun 25 2006
STATUS
approved