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A242398 Partial sums of the number of primes separating successive pairs of twin primes. 1
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 (list; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn
AUTHOR
Sam Mathers, Aug 16 2014
STATUS
approved

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Last modified May 23 21:14 EDT 2024. Contains 372765 sequences. (Running on oeis4.)