A061668 Numbers k such that x-4, x-2, x+2, x+4 are primes, where x = 30*k - 15.

1, 4, 7, 28, 50, 63, 70, 109, 116, 189, 315, 434, 522, 525, 536, 602, 631, 648, 701, 743, 844, 1058, 1162, 1460, 1712, 1845, 2100, 2241, 2317, 2408, 2576, 2657, 2702, 2758, 2961, 3262, 3305, 3371, 3662, 3885, 3977, 4074, 4516, 4806, 5243, 5524, 5562, 5706

Offset: 1

Author

Frank Ellermann, Jun 15 2001

Keywords

• easy
• nonn

Comments

Ignoring (5,7,11,13) another name for this sequence could be "twin prime twins".

Examples

			4 is in the sequence because 101, 103, 107, 109 are primes and 105 = 4*30 - 15.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

30 * a(n) = A007530(n+1) + 19.

Programs

Mathematica

p4Q[n_]:=Module[{c=30n-15},And@@PrimeQ[{c-4,c-2,c+2,c+4}]]; Select[ Range[ 6000],p4Q] (* Harvey P. Dale, Dec 04 2011 *)
Select[Range[6000], AllTrue[(30 # - 15) + {-4, -2, 2, 4}, PrimeQ] &] (* Michael De Vlieger, Jul 01 2018 *)

PARI

{ n=0; for (a=1, 391335, x=30*a - 15; if (isprime(x-4) && isprime(x-2) && isprime(x+2) && isprime(x+4), write("b061668.txt", n++, " ", a)) ) } \\ Harry J. Smith, Jul 26 2009

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 20 2001