A090835 Numbers n such that if p=prime(n), then p, p+6, p+12, p+18 are consecutive primes with p=6*k+5 for some k, where prime(n) denotes n-th prime.

54, 709, 821, 1510, 1594, 1726, 1842, 2009, 2600, 2876, 5689, 6252, 7438, 7728, 8090, 8229, 8654, 9105, 9184, 9997, 10934, 11343, 11390, 14193, 14866, 15000, 16320, 16748, 16950, 17246, 18466, 19164, 19802, 20152, 21508, 21692, 22048, 22270, 22997, 23242, 25435, 25466

Offset: 1

Author

Pierre CAMI, Dec 09 2003

Keywords

• easy
• nonn

Examples

			prime(54) = 251: 251, 257, 263, 269 are consecutive primes.
		

Crossrefs

Cf. A000040, A033451, A090832, A090833, A090834, A090836, A090837, A090838, A090839.

Programs

Mathematica

PrimePi/@Transpose[Select[Partition[Prime[Range[50000]],4,1],Differences[#]=={6, 6, 6}&&Mod[#[[1]],6]==5&]][[1]] (* Metin Sariyar, Sep 21 2019 *)

PARI

isok(n) = {my(p=prime(n), q, r, s); ((p % 6) == 5) && ((q=nextprime(p+1)) == p+6) && ((r=nextprime(q+1)) == p+12) && ((s=nextprime(r+1)) == p+18);} \\ Michel Marcus, Sep 20 2019

Extensions

a(9) corrected and more terms from Michel Marcus, Sep 20 2019