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

1,3

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

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for gaps between primes.

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.

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A035661 A287393 A260085 * A046930 A302254 A160409

Adjacent sequences: A159458 A159459 A159460 * A159462 A159463 A159464

Keyword

nonn

Author

Jaroslav Krizek, Apr 12 2009

Extensions

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

Status

approved