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

1,2

Comments

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

Links

Table of n, a(n) for n=1..105.

Eric Weisstein's World of Mathematics, Twin Prime Conjecture

Wikipedia, Twin prime

Formula

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

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

a(n) = 0 <=> { A079364 }. (End)

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 *)

Prog

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

Crossrefs

Cf. A000720, A014574, A079364, A090406.

Sequence in context: A212119 A096831 A191516 * A232654 A378396 A105971

Adjacent sequences: A168138 A168139 A168140 * A168142 A168143 A168144

Keyword

nonn

Author

Juri-Stepan Gerasimov, Nov 19 2009

Status

approved