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

Author

Sam Mathers, Aug 16 2014

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A001359, A006512. Partial sums of A204099.

Programs

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

Formula

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