A119753 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.

3, 5, 7, 11, 13, 19, 71, 73, 79, 139, 431, 433, 439, 499, 859, 4091, 4093, 4099, 4159, 4519, 8179, 86531, 86533, 86539, 86599, 86959, 90619, 173059, 513101, 513103, 513109, 513169, 513529, 517189, 599629, 1026199, 913571, 913573, 913579, 913639

Offset

1,1

Links

Table of n, a(n) for n=1..40.

Formula

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.

Example

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.

Maple

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;

Crossrefs

Sequence in context: A020587 A249077 A126960 * A169969 A291175 A174350

Adjacent sequences: A119750 A119751 A119752 * A119754 A119755 A119756

Keyword

nonn

Author

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

Status

approved