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%I #15 Mar 20 2020 10:35:29
%S 0,1,3,7,8,10,15,13,13,15,10,12,15,15,18,13,22,15,23,19,23,16,19,16,
%T 22,13,15,20,23,14,18,27,20,20,16,25,21,25,14,27,21,25,29,19,26,21,25,
%U 27,21,19,15,16,32,17,19,19,21,17,22,23,29,24,29,29,18,25,25
%N a(n) is the number of twin primes x-1,x+1 such that x=j*(p(n)#)/p(k), where 1 <= j < p(n+1) and 1 <= k <= n and p(k) doesn't divide j.
%C p(n) is the n-th prime; # denotes primorial (A002110).
%C a(n) seems to grow like 4*log(p(n)).
%e a(3) = 3 because for (j,k) = (1,3),(2,3),(3,3), j*(5#)/p(k)+-1 are primes.
%o (PARI) a(n) = {my(p=vector(n, i, prime(i)), x, y=prod(i=1, n, p[i])); sum(j=1, prime(n+1)-1, sum(k=1, n, j%p[k]>0 && ispseudoprime(x=j*y/p[k]-1) && ispseudoprime(x+2))); } \\ _Jinyuan Wang_, Mar 20 2020
%Y Cf. A002110, A087941, A088968.
%K nonn
%O 1,3
%A _Pierre CAMI_, Oct 25 2003
%E Edited by _Don Reble_, Nov 16 2005
%E More terms from _Jinyuan Wang_, Mar 20 2020
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