A177679 Numbers k such that 30*k and 60*k are both the average of twin prime pairs.

1, 22, 27, 71, 85, 111, 113, 195, 209, 351, 1106, 1387, 1471, 1785, 1848, 1911, 2128, 2170, 2346, 2366, 2409, 2470, 2492, 2626, 2689, 2731, 2918, 3108, 3410, 3849, 4159, 4466, 4565, 5214, 5382, 5615, 6117, 6161, 6559, 7035, 7063, 7349, 7469, 7798, 7923

Offset: 1

Author

Juri-Stepan Gerasimov, May 10 2010

Keywords

• nonn

Examples

			a(1)=1 because 30*1-1=29, 30*1+1=31, 60*1-1=59 and 60*1+1=61 are all twin primes.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A014574.

Programs

Magma

[k:k in [1..8000]|IsPrime(30*k-1) and IsPrime(30*k+1) and IsPrime(60*k-1) and IsPrime(60*k+1)]; // Marius A. Burtea, Dec 20 2019

Mathematica

Select[Range[8000], AllTrue[{30#-1, 30#+1, 60#-1, 60#+1}, PrimeQ] &] (* Amiram Eldar, Dec 20 2019 *)

Formula

a(n) = A066388(n+1)/30.

Extensions

Corrected (185 replaced by 195, 2718 replaced by 2918, 2731 inserted etc.) by R. J. Mathar, May 15 2010