

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.


4



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
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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



FORMULA

Let a(n) be the sequence defined recursively by a(1)=2 and a(n) is the first even 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)=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



STATUS

approved



