A163635 a(n) = 3*A022004(n) + 8.

23, 41, 59, 131, 311, 329, 581, 689, 941, 1049, 1391, 1931, 2471, 2579, 2651, 3281, 3839, 3911, 4289, 4451, 4469, 4829, 5621, 5999, 6251, 6719, 6809, 7979, 8069, 9761, 10391, 10589, 11021, 11759, 12011, 12389, 13559, 13919, 14369, 14801

Offset: 1

Author

Vincenzo Librandi, Aug 02 2009

Keywords

• nonn
• easy

Comments

Sum of the members of the n-th prime triple (p, p+2, p+6).

All terms are congruent to 5 (mod 18). See A242215. - Robert Bilinski, Sep 24 2019

Examples

			23 is in the sequence because 23 = 5+7+11 = 3*5+8.
41 is in the sequence because 41 = 11+13+17 = 3*11+8.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A022004, A073648, A098412.

Cf. A242215.

Programs

Magma

[(3*p+8): p in PrimesUpTo(1000)| IsPrime(p+6) and IsPrime(p+2)]; // Vincenzo Librandi, Jan 06 2018

Mathematica

8 + 3*Select[Prime[Range[1000]], PrimeQ[# + 2] && PrimeQ[# + 6] &] (* Vincenzo Librandi, Jan 04 2014 *)

PARI

is(n)=n%18==5 && isprime(n\3-2) && isprime(n\3) && isprime(n\3+4) \\ Charles R Greathouse IV, Jan 06 2018

Formula

a(n) = A022004(n) + (A022004(n)+2) + (A022004(n)+6);

a(n) = A022004(n) + A073648(n) + A098412(n).

Extensions

Notation normalized by R. J. Mathar, Aug 07 2009