A031165 a(n) = prime(n+3) - prime(n).

5, 8, 8, 10, 8, 10, 12, 12, 14, 12, 12, 10, 12, 16, 14, 14, 12, 12, 12, 12, 16, 18, 18, 14, 10, 8, 10, 20, 22, 24, 12, 18, 14, 18, 14, 16, 16, 16, 14, 18, 14, 16, 8, 18, 26, 28, 18, 10, 12, 12, 18, 18, 22, 18, 14, 14, 12, 12, 16, 26, 28, 20, 10, 20, 24, 30, 18, 16, 12

Offset: 1

Author

Jeff Burch, Dec 11 1999

Keywords

• nonn

Comments

Comments from Jonathan Vos Post, Jan 22 2006 (Start): This sequence is the k=3 case of the family of sequences a(k,n) = prime(n+k) - prime(n). See A001223 and A031131 for k = 1 and 2.

The records in this sequence give A115401. The minimal value, after the anomalous initial values (5, 8, 8), is 8 which occurs iff n is an element of A007530 (prime quadruples: numbers n such that n, n+2, n+6, n+8 are all prime). (End)

Examples

			a(1) = prime(4) - prime(1) = 7 - 2 = 5, which is the only odd element of this sequence.
a(2) = prime(5) - prime(2) = 11 - 3 = 8.
a(3) = prime(6) - prime(3) = 13 - 5 = 8.
a(4) = prime(7) - prime(4) = 17 - 7 = 10.
a(99) = prime(102) - prime(99) = 557 - 523 = 34. - _Jonathan Vos Post_, Jan 22 2006
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A001223, A007530, A031131, A034961, A115401.

Cf. A031166, A031167, A031168, A031169, A031170, A031171, A031172.

Programs

Haskell

a031165 n = a031165_list !! (n-1)
a031165_list = zipWith (-) (drop 3 a000040_list) a000040_list
-- Reinhard Zumkeller, Aug 23 2015

Magma

[NthPrime(n+3)-NthPrime(n): n in [1..100] ]; // Vincenzo Librandi, Apr 11 2011

Maple

a:= n-> ithprime(n+3)-ithprime(n): seq (a(n), n=1..80);

Mathematica

t = Array[Prime, 75]; Drop[t, 3] - Drop[t, -3] (* Robert G. Wilson v *)
#[[4]]-#[[1]]&/@Partition[Prime[Range[80]],4,1] (* Harvey P. Dale, Nov 07 2021 *)

PARI

p=2;q=3;r=5;forprime(s=7,1e3,print1(s-p", "); p=q;q=r;r=s) \\ Charles R Greathouse IV, Nov 07 2012

Formula

a(n) = prime(n+3) - prime(n). a(n) = A000040(n+3) - A000040(n). - Jonathan Vos Post, Jan 22 2006

a(n) = A034961(n+1) - A034961(n). - Zak Seidov, Nov 07 2012

Extensions

Edited by R. J. Mathar and N. J. A. Sloane, Aug 11 2008