A046930 Size of sea of composite numbers surrounding n-th prime.

1, 1, 2, 4, 4, 4, 4, 4, 8, 6, 6, 8, 4, 4, 8, 10, 6, 6, 8, 4, 6, 8, 8, 12, 10, 4, 4, 4, 4, 16, 16, 8, 6, 10, 10, 6, 10, 8, 8, 10, 6, 10, 10, 4, 4, 12, 22, 14, 4, 4, 8, 6, 10, 14, 10, 10, 6, 6, 8, 4, 10, 22, 16, 4, 4, 16, 18, 14, 10, 4, 8, 12, 12, 10, 8, 8, 12, 10, 10, 16, 10, 10, 10, 6, 8, 8

Offset: 1

Author

N. J. A. Sloane, Marc LeBrun

Keywords

• nonn
• easy
• nice

Examples

			23 is in a sea of 8 composites: 20,21,22,23,24,25,26,27,28.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Related sequences: A023186-A023188, A046929-A046931, A051650, A051652, A051697-A051702, A051728-A051730.

Programs

Haskell

a046930 1 = 1
a046930 n = subtract 2 $ a031131 n  -- Reinhard Zumkeller, Dec 19 2013

Maple

[ seq(ithprime(i)-ithprime(i-2)-2,i=3..100) ];

Mathematica

Table[ Prime[n + 2] - Prime[n] - 2, {n, 75}] (* Robert G. Wilson v Oct 27 2004 *)
Join[{1},#[[3]]-#[[1]]-2&/@Partition[Prime[Range[90]],3,1]] (* Harvey P. Dale, Sep 26 2012 *)

Formula

a(n) = A031131(n) - 2 for n > 1. - Reinhard Zumkeller, Dec 19 2013

Extensions

More terms from Michel ten Voorde