A122170 Number of primes p <= 2n such that p+n is also a prime.

1, 1, 1, 2, 1, 3, 0, 3, 1, 4, 1, 5, 0, 4, 1, 4, 1, 6, 0, 4, 1, 4, 0, 10, 0, 6, 1, 5, 1, 12, 0, 5, 0, 6, 1, 13, 0, 7, 1, 9, 1, 13, 0, 7, 1, 6, 0, 13, 0, 9, 1, 7, 0, 14, 0, 12, 1, 7, 1, 19, 0, 7, 0, 10, 1, 20, 0, 11, 1, 13, 1, 15, 0, 8, 0, 10, 1, 18, 0, 12, 1, 8, 0, 23, 0, 10, 1, 10, 0, 26, 0, 13, 0, 13

Offset

1,4

Comments

a(n)=0 for n in A007921.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(12)=5 because only the 5 primes p=5,7,11,17,19 below 24 form other primes p+12 = 17,19,23,29,31.

Maple

P:= select(isprime, [2, seq(i, i=3..3000, 2)]);
f:= proc(n) local m, R;
  m:= ListTools:-BinaryPlace(P, 3*n);
  R:= convert(P[1..m], set);
  nops((R -~ n) intersect R)
end proc:
f(1):= 1:
map(f, [$1..1000]); # Robert Israel, Mar 22 2023

Mathematica

Table[Length[Select[Select[Range[2*n], PrimeQ], PrimeQ[ #+n]&]], {n, 100}] (* Ryan Propper, Nov 12 2006 *)

Crossrefs

Sequence in context: A146094 A098035 A079055 * A066029 A141198 A239621

Adjacent sequences: A122167 A122168 A122169 * A122171 A122172 A122173

Keyword

nonn

Author

Lekraj Beedassy, Aug 23 2006

Extensions

More terms from Ryan Propper, Nov 12 2006

Status

approved