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.

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

Offset

0,1

Comments

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

Links

Michael De Vlieger, Table of n, a(n) for n = 0..10000

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

Cf. A001359, A078859.

Sequence in context: A133723 A324279 A222464 * A217518 A364091 A257928

Adjacent sequences: A095386 A095387 A095388 * A095390 A095391 A095392

Keyword

nonn

Author

Labos Elemer and Enoch Haga, Jun 15 2004

Status

approved