

A095389


a(n) is the number of residues from reduced residue system, R, modulo 210 such that both R and R+2 are primes, i.e., both 210n+r and 210n+r+2 are primes at fixed n.


6



13, 7, 6, 5, 5, 4, 6, 5, 5, 6, 6, 2, 6, 2, 3, 6, 7, 3, 4, 6, 6, 4, 5, 4, 2, 3, 6, 4, 1, 4, 2, 5, 5, 3, 4, 4, 2, 2, 2, 4, 3, 2, 5, 2, 5, 2, 4, 4, 3, 5, 2, 2, 4, 2, 3, 2, 4, 4, 3, 1, 1, 4, 1, 2, 0, 6, 5, 2, 3, 4, 1, 0, 4, 1, 5, 1, 4, 3, 1, 3, 3, 3, 3, 3, 5, 7, 3, 2, 2, 0, 3, 3, 4, 2, 3, 4, 2, 4, 4, 3, 4, 2, 6, 3, 1
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OFFSET

0,1


COMMENTS

Since arbitrarily large prime gaps occur, several consecutive zeros may arise in the sequence.


LINKS



EXAMPLE

n=0: only 13+2=15 integers correspond to the condition: {11,17,29,41,59,71,101,107,137,149,179,191,197}, so a[0]=13; see A078859.
n=11: only 2 twins were found, {2339,2341} and {2381,2383} corresponding to residue pairs {29,31} and {71,73}.


MATHEMATICA

{k =0, ta=Table[0, {100}]}; Do[{m=0}; Do[s=210k+r; s1=210k+r+2; If[PrimeQ[s]&&PrimeQ[s+2], m=m+1], {r, 1, 210}]; ta[[k]]=m, {k, 1, 100}]; ta
(* Second program: *)
With[{P = Product[Prime@ i, {i, 4}]}, Function[R, Array[Count[R + P #, k_ /; Times @@ Boole@ PrimeQ@ {k, k + 2} == 1] &, 105, 0]]@ Select[Partition[Select[Range[P + 1], CoprimeQ[#, P] &], 2, 1], Differences@ # == {2} &][[All, 1]]] (* Michael De Vlieger, May 15 2017 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



