

A087941


a(n) is the number of consecutive primes x2,x+2 such that x=j*(p(n)#/2)/p(k), where 1 <= j < p(n+1) and 2 <= k <= n and p(k) doesn't divide j.


2



0, 0, 1, 3, 7, 4, 4, 6, 7, 9, 7, 8, 8, 6, 9, 9, 7, 7, 6, 10, 9, 10, 5, 9, 10, 5, 8, 10, 13, 8, 15, 7, 6, 13, 8, 7, 8, 14, 13, 13, 11, 11, 7, 11, 10, 8, 11, 5, 11, 12, 14, 6, 16, 14, 15, 15, 12, 9, 7, 7, 13, 11, 10, 12, 12, 10, 13, 11, 7, 14, 14, 13, 14, 10, 13
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OFFSET

1,4


COMMENTS

p(n) is the nth prime; # denotes primorial (A002110).
a(n) seems to grow like 2*log(p(n)).


LINKS

Table of n, a(n) for n=1..75.


EXAMPLE

a(4) = 3 because for (j,k) = (1,3),(1,4),(3,4), j*(7#/2)/p(k)+2 are consecutive primes.


PROG

(PARI) a(n) = {my(p=vector(n, i, prime(i)), x, y=prod(i=2, n, p[i])); sum(j=1, prime(n+1)1, sum(k=2, n, j%p[k]>0 && ispseudoprime(x=j*y/p[k]2) && nextprime(x+1)==x+4)); } \\ Jinyuan Wang, Mar 20 2020


CROSSREFS

Cf. A002110, A087859, A088968.
Sequence in context: A266273 A256676 A267412 * A278389 A021271 A238274
Adjacent sequences: A087938 A087939 A087940 * A087942 A087943 A087944


KEYWORD

nonn


AUTHOR

Pierre CAMI, Oct 27 2003


EXTENSIONS

Edited by Don Reble, Nov 16 2005
More terms from Jinyuan Wang, Mar 20 2020


STATUS

approved



