A242398 Partial sums of the number of primes separating successive pairs of twin primes.

0, 0, 0, 1, 2, 4, 5, 9, 9, 12, 12, 16, 16, 16, 18, 19, 22, 23, 25, 28, 38, 38, 42, 49, 53, 56, 58, 59, 61, 79, 79, 79, 81, 83, 100, 100, 101, 101, 103, 109, 118, 121, 122, 123, 124, 132, 135, 137, 137, 152, 153, 157, 158, 159, 166, 173, 173, 177, 177, 181, 184, 188, 188, 189, 189, 190, 197, 199, 204, 205, 210

Offset

1,5

Comments

a(n) is the number of primes that are not twin primes greater than the first twin prime pair (3,5) and less than the (n+1)th twin prime pair. All primes, other than two either exist in one of the twin prime pairs or are counted in the sum. Two is not included because it occurs before the first twin prime pair.

Links

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Example

For n=4, a(4)=1. We can get this by writing the first n+1 twin prime pairs and taking the sum of the primes in between them. The pairs are (3,5),(5,7),(11,13),(17,19),(29,31). The only prime between these pairs is 23, thus the answer is one.

Prog

(PARI) s=0; forprime(p=5, 10^4, if(isprime(p+2), print1(s", "); s--, s++)) \\ Jens Kruse Andersen, Aug 17 2014

Crossrefs

Partial sum of A048614.

Sequence in context: A359878 A270097 A167511 * A174112 A111490 A079784

Adjacent sequences: A242395 A242396 A242397 * A242399 A242400 A242401

Keyword

nonn

Author

Sam Mathers, Aug 16 2014

Status

approved