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

Author

Eric W. Weisstein, Nov 29 2003

Keywords

• nonn
• easy

Comments

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

Links

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

Crossrefs

Cf. A000720, A080545, A090406.

Programs

Maple

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

Mathematica

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 *)

PARI

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

Python

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

Python

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