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A087941
a(n) is the number of consecutive primes x-2,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
OFFSET
1,4
COMMENTS
p(n) is the n-th prime; # denotes primorial (A002110).
a(n) seems to grow like 2*log(p(n)).
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
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