A120403 a(1)=3; a(n)=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 1<=i<=n-1.

3, 9, 15, 45, 225, 639, 1275, 4005, 675405, 2203959, 3075159, 6195234165, 77989711185, 4566262987329

Offset: 1

Author

Walter Kehowski, Jul 02 2006

Keywords

• nonn
• more

Comments

All elements are 3 mod 6. In base 12 the sequence is 3, 9, 13, 39, 169, 453, 8X3, 2399, 286X39, 8X3533, 1043733, where X is 10 and E is eleven.

Examples

			a(2)=9 since 9 is the first odd number > a(1)=3 such that 2*9-1=17 is prime and 9+3-1=13 is prime.
		

Crossrefs

Cf. A119752, A119754 (resulting primes), A119751, A119753, A103828.

Programs

Maple

OP:=[3]: for w to 1 do for k from 0 to 12^8 do n:=6*k+3; p:=2*n-1; Q:=map(z-> z+n-1, OP); if isprime(p) and andmap(isprime,Q) then OP:=[op(OP), n]; print(n); fi od od;

Formula

a(1)=3; a(n) = s where s is the first odd number s>a(n-1) such that 2*s-1 is prime and s+a(i)-1 is prime, 1<=i<=n-1.

a(n) = A119752(n) + 1. - Chandler

Extensions

a(12)-a(14) from Ray Chandler, Apr 04 2010