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

1,1

Links

Table of n, a(n) for n=1..22.

Formula

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

Example

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).

Prog

(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

Crossrefs

Subsequence of A089450.

Cf. A089007, A089009, A089524.

Sequence in context: A236117 A255694 A366890 * A253034 A328563 A250517

Adjacent sequences: A089489 A089490 A089491 * A089493 A089494 A089495

Keyword

nonn

Author

Ray Chandler, Nov 04 2003

Extensions

Offset changed to 1 by Jinyuan Wang, Aug 06 2021

Status

approved