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A242757 Partial sums of the number of integers between successive twin prime pairs. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 17 13:33 EST 2019. Contains 329230 sequences. (Running on oeis4.)