A120402 a(1)=2; a(n)=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 1<=i<=n-1.

2, 4, 10, 70, 430, 4090, 86530, 513100, 913570, 7914340, 6593621380, 9366241600

Offset: 1

Author

Walter Kehowski, Jul 02 2006

Keywords

• more
• nonn

Comments

All elements after the first are 4 mod 6. In base 12 the sequence is 2, 4, X, 5X, 2EX, 244X, 420XX, 208E24, 38082X, 2798084, where X is 10 and E is eleven.

Examples

			a(2)=4 since 4 is the first even number > a(1)=2 such that 2*4-1=7 is prime and 4+2-1=5 is prime.
		

Crossrefs

Cf. A119752, A119754, A119751, A119753, A103828.

Programs

Maple

EP:=[2]: for w to 1 do for k from 0 to 12^8 do n:=6*k+4; p:=2*n-1; Q:=map(z-> z+n-1, EP); if isprime(p) and andmap(isprime,Q) then EP:=[op(EP),n]; print(n); fi od od;

Formula

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

Extensions

a(11)-a(12) from Bert Dobbelaere, Apr 17 2019