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Partial sums of the number of integers between successive twin prime pairs.
1

%I #27 Nov 02 2014 12:18:37

%S 0,3,6,15,24,39,48,75,78,105,114,141,150,153,180,189,216,225,252,285,

%T 354,363,390,447,492,519,534,555,570,717,726,729,756,777,912,921,936,

%U 945,972,1029,1104,1149,1158,1167

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

%C 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.

%H Jens Kruse Andersen, <a href="/A242757/b242757.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A001359(n+1) - 2 - 3*n. - _Robert Israel_, Aug 17 2014

%e 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.

%o (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

%Y Cf. A001359, A006512. Partial sums of A204099.

%K nonn

%O 1,2

%A _Sam Mathers_, Aug 16 2014