A089492 Sequence of primes 2*p(k) + 3 such that 2*p(k) + 3, 2*p(k+1) + 3, 2*p(k+2) + 3, 2*p(k+3) + 3 are consecutive primes, where p(i) denotes the i-th prime.

1552237, 4315469, 8774137, 9629197, 10048081, 10875149, 11469389, 14498741, 18280861, 18789629, 19309957, 19309981, 25386029, 27265457, 28398641, 29697029, 31298269, 31355297, 36792901, 47318969, 47487889, 55449689

Offset: 1

Author

Ray Chandler, Nov 04 2003

Keywords

• nonn

Examples

			p(62178)=776117, 2*776117 + 3 = 1552237 = p(117814);
p(62179)=776119, 2*776119 + 3 = 1552241 = p(117815);
p(62180)=776137, 2*776137 + 3 = 1552277 = p(117816);
p(62181)=776143, 2*776143 + 3 = 1552289 = p(117817).
		

Crossrefs

Subsequence of A089450.

Cf. A089007, A089009, A089524.

Programs

PARI

a089492(limit)={my(pv=[2,3,5,0],v3=[3,3,3,3],ks(k)=2*k+3);forprime(p=7,limit,pv[4]=p;if(vecsum(isprime(2*pv+v3))==4&&primepi(ks(pv[4]))-primepi(ks(pv[1]))==3,print1(ks(pv[1]),", "));pv[1]=pv[2];pv[2]=pv[3];pv[3]=pv[4])};
a089492(30000000) \\ Hugo Pfoertner, Aug 06 2021

Formula

a(n) = 2*A089007(n) + 3 = 2*A000040(A089009(n)) + 3 = A000040(A089524(n)).

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 06 2021