A127567 Given k, the product of the first n primes and starting with the first prime at least 3 greater than k, a(n) is the number of consecutive primes where p-k is also prime.

2, 6, 10, 19, 25, 29, 36, 42, 43, 41, 63, 65, 45, 69, 86, 98, 90, 77, 94, 132, 118, 112, 132, 120, 131, 133, 150, 128, 203, 220, 163, 175, 161, 176, 168, 171, 206, 233, 236, 250, 201, 230, 293, 270, 297, 283, 256, 253, 272, 318, 266, 277, 296, 308, 349, 353, 312

Offset

1,1

Links

Table of n, a(n) for n=1..57.

http://h.xerol.org/f/1primecheck.txtShows applicable sequences of primes for n = 2..9

Example

For n = 2, k = 2*3 = 6. The first prime at least 3 greater than 6 is 11.
11-6 = 5, 13-6 = 7, 17-6 = 11, 19-6 = 13, 23-6 = 17, 29-6 = 23, all of which are primes. 31-6 = 25 is not prime, so a(2) = 6 because there are 6 prime terms.

Maple

with(numtheory): a:=proc(n) local k, p, c, ct, j: k:=product(ithprime(i), i=1..n); p:=nextprime(k+2); c:=pi(p): ct:=0: for j from c while isprime(ithprime(j)-k)=true do ct:=ct+1: od: ct; end: seq(a(n), n=1..9); # Emeric Deutsch, Apr 13 2007

Crossrefs

Sequence in context: A006553 A370048 A054273 * A360420 A169643 A005993

Adjacent sequences: A127564 A127565 A127566 * A127568 A127569 A127570

Keyword

nonn

Author

Ellis M. Eisen (xerol(AT)xerol.org), Apr 02 2007

Extensions

Corrected by Emeric Deutsch, Apr 13 2007

More terms from R. J. Mathar, Sep 23 2007

Status

approved