A168141 a(n) = pi(n + 1) - pi(n - 2), where pi is the prime counting function.

1, 2, 2, 2, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 2, 1, 1, 0

Offset: 1

Author

Juri-Stepan Gerasimov, Nov 19 2009

Keywords

• nonn

Comments

Conjecture: a(n) = 2 for infinitely many n. This is equivalent to the twin prime conjecture. - Andrew Slattery, Apr 26 2020

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Eric Weisstein's World of Mathematics, Twin Prime Conjecture
• Wikipedia, Twin prime

Crossrefs

Cf. A000720, A014574, A079364, A090406.

Programs

Maple

A168141 := proc(n) numtheory[pi](n+1)-numtheory[pi](n-2) ; end proc: seq(A168141(n),n=1..120) ; # R. J. Mathar, Nov 19 2009
# second Maple program:
a:= n-> add(`if`(isprime(n+i), 1, 0), i=-1..1):
seq(a(n), n=1..120);  # Alois P. Heinz, Apr 28 2020

Mathematica

Table[PrimePi[n + 1] - PrimePi[n - 2], {n, 100}] (* Wesley Ivan Hurt, Apr 26 2020 *)

PARI

a(n) = primepi(n+1) - primepi(n-2); \\ Michel Marcus, Apr 27 2020

Formula

From Alois P. Heinz, Apr 28 2020: (Start)

a(n) = 2 <=> n in { 2,3 } union { A014574 }.

a(n) = 0 <=> n in A079364. (End)