A164133 Primes p such that 4*p and 6*p are each the sum of two consecutive primes.

2, 3, 13, 43, 127, 167, 613, 647, 1033, 1483, 1543, 2297, 2927, 3701, 3823, 4463, 5101, 5417, 5657, 6133, 8081, 9227, 11273, 11833, 12511, 13291, 13873, 17627, 19853, 20011, 21313, 21727, 22193, 23041, 23059, 23081, 23159, 24443, 26347, 26947, 27407, 27527

Offset: 1

Author

Juri-Stepan Gerasimov, Aug 11 2009

Keywords

• nonn

Examples

			p=13 is in the sequence because 4*13 = 52 = A001043(9) and 6*13 = 78 = A001043(12) are both in A001043.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3000

Crossrefs

Cf. A000040, A118134, A163487.

Programs

Maple

P:= select(isprime, [2,seq(i,i=3..10^6)]):
PS:= P[1..-2] + P[2..-1]:
convert(P,set) intersect convert(1/4 * PS, set) intersect convert(1/6*PS,set); # Robert Israel, Dec 08 2024

Mathematica

stcpQ[n_]:=Module[{a=4n,b=6n},a==NextPrime[a/2]+NextPrime[a/2,-1]&&b== NextPrime[b/2]+NextPrime[b/2,-1]]; Select[Prime[Range[3100]],stcpQ] (* Harvey P. Dale, May 01 2019 *)

Formula

A163487 INTERSECT A118134.

Extensions

Extended by R. J. Mathar, Aug 27 2009