A159461 Numbers of previous and following composites of n-th prime.

0, 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

Offset: 1

Author

Jaroslav Krizek, Apr 12 2009

Keywords

• nonn

Comments

Essentially the same as A046930. - R. J. Mathar, Apr 16 2009

For twin primes this is the gap before or after the twins, e.g., a(17) = 6 = 59 - 53 = prime(17) - prime(16) for the twin (59, 61) with a(18) = 6 = 67 - 61 = prime(19) - prime(18). - Frank Ellermann, Mar 17 2020

Examples

			For a(16) = 10 = 59 - 47 - 2 = prime(16+1) - prime(16-1) - 2 is the sum of the prime gaps minus two ending and starting at prime(16) = 53.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for gaps between primes.

Crossrefs

Cf. A000040, A001223, A046933, A008578, A158611.

Programs

Mathematica

Join[{0},Total[Differences[#]-1]&/@Partition[Prime[Range[60]],3,1]] (* Harvey P. Dale, Nov 27 2011 *)

Formula

For n >= 2, we have

a(n) = A001223(n) + A001223(n-1) - 2;

a(n) = A046933(n) + A046933(n-1);

a(n) = A008578(n+2) - A008578(n) - 2;

a(n) = A158611(n+3) - A158611(n+1) - 2.

Extensions

Correction for change of offset in A158611 and A008578 in Aug 2009 Jaroslav Krizek, Jan 27 2010