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%I #26 May 18 2020 07:03:04
%S 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,
%T 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,
%U 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
%N a(n) = pi(n + 1) - pi(n - 2), where pi is the prime counting function.
%C Conjecture: a(n) = 2 for infinitely many n. This is equivalent to the twin prime conjecture. - _Andrew Slattery_, Apr 26 2020
%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimeConjecture.html">Twin Prime Conjecture</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Twin_prime#Other_theorems_weaker_than_the_twin_prime_conjecture">Twin prime</a>
%F From _Alois P. Heinz_, Apr 28 2020: (Start)
%F a(n) = 2 <=> n in { 2,3 } union { A014574 }.
%F a(n) = 0 <=> { A079364 }. (End)
%p 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
%p # second Maple program:
%p a:= n-> add(`if`(isprime(n+i), 1, 0), i=-1..1):
%p seq(a(n), n=1..120); # _Alois P. Heinz_, Apr 28 2020
%t Table[PrimePi[n + 1] - PrimePi[n - 2], {n, 100}] (* _Wesley Ivan Hurt_, Apr 26 2020 *)
%o (PARI) a(n) = primepi(n+1) - primepi(n-2); \\ _Michel Marcus_, Apr 27 2020
%Y Cf. A000720, A014574, A079364, A090406.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Nov 19 2009
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