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%I #14 Mar 20 2020 10:35:43
%S 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,
%T 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,
%U 9,7,7,13,11,10,12,12,10,13,11,7,14,14,13,14,10,13
%N 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.
%C p(n) is the n-th prime; # denotes primorial (A002110).
%C a(n) seems to grow like 2*log(p(n)).
%e a(4) = 3 because for (j,k) = (1,3),(1,4),(3,4), j*(7#/2)/p(k)+-2 are consecutive primes.
%o (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
%Y Cf. A002110, A087859, A088968.
%K nonn
%O 1,4
%A _Pierre CAMI_, Oct 27 2003
%E Edited by _Don Reble_, Nov 16 2005
%E More terms from _Jinyuan Wang_, Mar 20 2020
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