A242757 Partial sums of the number of integers between successive twin prime pairs.

0, 3, 6, 15, 24, 39, 48, 75, 78, 105, 114, 141, 150, 153, 180, 189, 216, 225, 252, 285, 354, 363, 390, 447, 492, 519, 534, 555, 570, 717, 726, 729, 756, 777, 912, 921, 936, 945, 972, 1029, 1104, 1149, 1158, 1167

Offset

1,2

Comments

a(n) is the partial sum of the number of integers separating each successive pair of twin prime numbers less than and up to the n-th pair of twin primes.

Links

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

Formula

a(n) = A001359(n+1) - 2 - 3*n. - Robert Israel, Aug 17 2014

Example

For n=4, a(4)=15 because the number of integers separating the first 4 pairs of twin prime numbers are as follows, 0 between (3,5) and (5,7), 3 between (5,7) and (11,13), 3 between (11,13) and (17,19), and 9 between (17,19) and (29,31). 0+3+3+9=15 so a(4)=15.

Prog

(PARI) s=0; q=2; forprime(p=5, 10^4, if(isprime(p+2), s=s+p-q-3; print1(s", "); q=p)) \\ Jens Kruse Andersen, Aug 17 2014

Crossrefs

Cf. A001359, A006512. Partial sums of A204099.

Sequence in context: A044888 A179805 A006639 * A166448 A192171 A281758

Adjacent sequences: A242754 A242755 A242756 * A242758 A242759 A242760

Keyword

nonn

Author

Sam Mathers, Aug 16 2014

Status

approved