A090405 - OEIS

%I #28 May 07 2021 17:52:34

%S 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,

%T 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,

%U 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

%N a(n) = PrimePi(n+2) - PrimePi(n).

%C For n>1, a(n) = 1 if n+1 or n+2 is prime, otherwise a(n) = 0. - _Robert Israel_, Mar 30 2017

%H G. C. Greubel, <a href="/A090405/b090405.txt">Table of n, a(n) for n = 1..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Hardy-LittlewoodConjectures.html">Hardy-Littlewood Conjectures</a>

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

%t Table[Subtract @@ Map[PrimePi, n + {2, 0}], {n, 120}] (* or *)

%t Table[Boole@ PrimeQ[n + 1 + Boole[OddQ@ n]] + Boole[n == 1], {n, 120}] (* _Michael De Vlieger_, Mar 30 2017 *)

%o (PARI) for(n=1, 100, print1(primepi(n + 2) - primepi(n),", ")) \\ _Indranil Ghosh_, Mar 31 2017

%o (Python)

%o from sympy import primepi

%o print([primepi(n + 2) - primepi(n) for n in range(1, 101)])

%o # _Indranil Ghosh_, Mar 31 2017

%o (Python)

%o from sympy import isprime

%o def a(n):

%o     if n<2: return 2

%o     else:

%o         if isprime(n + 1 + (n%2 == 1) + (n==1)): return 1

%o         else: return 0 # _Indranil Ghosh_, Mar 31 2017

%Y Cf. A000720, A080545, A090406.

%K nonn,easy

%O 1,1

%A _Eric W. Weisstein_, Nov 29 2003