A119754 Prime numbers in their order of occurrence and generated by A119752, the sequence of even numbers defined recursively by a(1)=2 and a(i) + a(j) + 1 is prime for all i,j.

5, 11, 17, 17, 23, 29, 47, 53, 59, 89, 227, 233, 239, 269, 449, 641, 647, 653, 683, 863, 1277, 1277, 1283, 1289, 1319, 1499, 1913, 2549, 4007, 4013, 4019, 4049, 4229, 4643, 5279, 8009, 675407, 675413, 675419, 675449, 675629, 676043, 676679, 679409

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.

Links

Table of n, a(n) for n=1..44.

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

Sequence in context: A123082 A084037 A077130 * A239127 A220432 A266420

Adjacent sequences: A119751 A119752 A119753 * A119755 A119756 A119757

Keyword

nonn

Author

Walter Kehowski, Jun 17 2006, Jun 19 2006, Jun 25 2006

Status

approved