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

1,2

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

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A005097, A014545.

Sequence in context: A127644 A324283 A161338 * A007783 A363128 A050625

Adjacent sequences: A047844 A047845 A047846 * A047848 A047849 A047850

Keyword

easy,nonn

Author

Enoch Haga

Extensions

Corrected by Henry Bottomley, Jul 18 2000

Status

approved