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 A218867 Number of prime pairs {p,q} with p>q and {p-4,q+4} also prime such that p+(1+(n mod 6))q=n if n is not congruent to 4 (mod 6), and p-q=n and q
 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 2, 0, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 1, 2, 0, 1, 2, 2, 2, 2, 0, 2, 2, 1, 1, 1, 2, 1, 0, 0, 1, 0, 2, 2, 0, 2, 1, 3, 0, 1, 1, 2, 2, 1, 0, 3, 2, 3, 0, 2, 1, 4, 1, 1, 2, 1, 3, 2 (list; graph; refs; listen; history; text; internal format)
 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 Zhi-Wei Sun, Table of n, a(n) for n = 1..10000 Zhi-Wei Sun, Conjectures involving primes and quadratic forms, arXiv:1211.1588. Zhi-Wei Sun, Table of n, a(n) for n = 1..10^5. EXAMPLE a(20)=1 since 20=11+3*3 with 11-4 and 3+4 prime. a(28)=1 since 28=41-13 with 41-4 and 13+4 prime. MATHEMATICA c[n_]:=c[n]=If[Mod[n+2, 6]==0, 1, -1-Mod[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[(n-1)/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 Zhi-Wei Sun, Nov 13 2012 STATUS approved

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Last modified January 18 05:09 EST 2020. Contains 330995 sequences. (Running on oeis4.)