

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.


4



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
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OFFSET

1,1


LINKS



FORMULA

Let a(n) be the sequence defined recursively by a(1)=1 and a(n) is the first odd number greater than a(n1) such that 2*a(n)+1 is prime and a(i) + a(n) + 1 is prime for all i<=n1. Then p(n) is the nth 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



KEYWORD

nonn


AUTHOR



STATUS

approved



