

A218867


Number of prime pairs {p,q} with p>q and {p4,q+4} also prime such that p+(1+(n mod 6))q=n if n is not congruent to 4 (mod 6), and pq=n and q<n/2 if n=4 (mod 6).


10



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OFFSET

1,30


COMMENTS

Conjecture: a(n)>0 for all n>50000 with n different from 50627, 61127, 66503.
This conjecture implies that there are infinitely many cousin prime pairs. It is similar to the conjectures related to A219157 and A219055.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000
ZhiWei Sun, Conjectures involving primes and quadratic forms, arXiv:1211.1588.
ZhiWei Sun, Table of n, a(n) for n = 1..10^5.


EXAMPLE

a(20)=1 since 20=11+3*3 with 114 and 3+4 prime. a(28)=1 since 28=4113 with 414 and 13+4 prime.


MATHEMATICA

c[n_]:=c[n]=If[Mod[n+2, 6]==0, 1, 1Mod[n, 6]]; d[n_]:=d[n]=2+If[Mod[n+2, 6]>0, Mod[n, 6], 0]; a[n_]:=a[n]=Sum[If[PrimeQ[Prime[k]+4] == True && PrimeQ[n+c[n]Prime[k]] == True && PrimeQ[n+c[n]Prime[k]4]==True, 1, 0], {k, 1, PrimePi[(n1)/d[n]]}]; Do[Print[n, " ", a[n]], {n, 100}]


CROSSREFS

Cf. A023200, A046132, A219157, A219055, A002375, A046927, A218754, A218825, A219052.
Sequence in context: A079483 A262115 A071460 * A295664 A250213 A033794
Adjacent sequences: A218864 A218865 A218866 * A218868 A218869 A218870


KEYWORD

nonn


AUTHOR

ZhiWei Sun, Nov 13 2012


STATUS

approved



