A047847 Numbers n such that n + (n+1) and (n+2) + (n+3) are both prime.

1, 3, 6, 9, 18, 21, 33, 39, 48, 51, 54, 63, 81, 96, 111, 114, 138, 153, 156, 174, 189, 198, 219, 228, 231, 243, 249, 306, 321, 336, 369, 378, 384, 411, 426, 429, 438, 441, 453, 468, 483, 504, 543, 546, 606, 639, 648, 651, 711, 714, 723, 741, 744, 774, 783, 789

Offset: 1

Author

Enoch Haga

Keywords

• easy
• nonn

Comments

Except for the first one, all terms are multiples of 3, as can be seen from the formula a(n+1) = 3*A056956(n). - Zak Seidov, Aug 26 2012

Examples

			If n = 6, then 6 + 7 = 13 and 8 + 9 = 17 are both prime.
		

Links

• Jayanta Basu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005097, A014545.

Programs

Mathematica

Select[Range[790], And @@ PrimeQ[{2*# + 1, 2*# + 5}] &] (* Jayanta Basu, Aug 11 2013 *)
Select[Range[800],AllTrue[2#+{1,5},PrimeQ]&] (* Harvey P. Dale, Jan 28 2023 *)

PARI

is_A047847(n)=isprime(n*2+1)&isprime(n*2+5)  \\ - M. F. Hasler, Aug 26 2012

Formula

a(n) = (A023200(n)-1)/2 = (A046132(n)-5)/2 = 3*A056956(n-1) (for n>1).

Extensions

Corrected by Henry Bottomley, Jul 18 2000