A090406 -id:A090406 - cp's OEIS frontend

A090405 a(n) = PrimePi(n+2) - PrimePi(n).

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

Offset: 1

Eric W. Weisstein, Nov 29 2003

For n>1, a(n) = 1 if n+1 or n+2 is prime, otherwise a(n) = 0. - Robert Israel, Mar 30 2017

G. C. Greubel, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Hardy-Littlewood Conjectures

Cf. A000720, A080545, A090406.

with(numtheory): A090405:=n->pi(n+2)-pi(n): seq(A090405(n), n=1..150); # Wesley Ivan Hurt, Mar 30 2017

Table[Subtract @@ Map[PrimePi, n + {2, 0}], {n, 120}] (* or *)
Table[Boole@ PrimeQ[n + 1 + Boole[OddQ@ n]] + Boole[n == 1], {n, 120}] (* Michael De Vlieger, Mar 30 2017 *)

for(n=1, 100, print1(primepi(n + 2) - primepi(n),", ")) \\ Indranil Ghosh, Mar 31 2017

from sympy import primepi
print([primepi(n + 2) - primepi(n) for n in range(1, 101)])
# Indranil Ghosh, Mar 31 2017

from sympy import isprime
def a(n):
    if n<2: return 2
    else:
        if isprime(n + 1 + (n%2 == 1) + (n==1)): return 1
        else: return 0 # Indranil Ghosh, Mar 31 2017

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

Original entry on oeis.org

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

Juri-Stepan Gerasimov, Nov 19 2009

nonn

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

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

Cf. A000720, A014574, A079364, A090406.

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

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

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

From Alois P. Heinz, Apr 28 2020: (Start)
a(n) = 2 <=> n in { 2,3 } union { A014574 }.
a(n) = 0 <=> n in A079364. (End)

cp's OEIS Frontend

A090405 a(n) = PrimePi(n+2) - PrimePi(n).

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