

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 pk is also prime.


0



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
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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.
116 = 5, 136 = 7, 176 = 11, 196 = 13, 236 = 17, 296 = 23, all of which are primes. 316 = 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: A084481 A006553 A054273 * A169643 A005993 A028247
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



