A292438 Characteristic function of non-isolated nonprimes.

1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Wesley Ivan Hurt, Mar 31 2018

Keywords

• nonn

Comments

Non-isolated nonprimes in the sense that at least one of the two adjacent integers is also a nonprime.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65539
• Index entries for characteristic functions

Crossrefs

Cf. A000720, A010051, A014574, A141468, A164276.

Programs

Mathematica

a[0] = 1; a[1] = 1; a[2] = 0; a[n_] := 1 - (PrimePi[n - Mod[n + 1, 2]] - PrimePi[n - Mod[n + 1, 2] - 1]) (PrimePi[n + Mod[n + 1, 2]] - PrimePi[n + Mod[n + 1, 2] - 1]); Table[a[n], {n, 0, 100}]

PARI

A292438(n) = if(n<2,1,!isprime(n)&&((!isprime(n-1))||(!isprime(n+1)))); \\ Antti Karttunen, Jul 02 2018

Formula

a(0)=1, a(1)=1, a(2)=0, a(n) = 1 - A010051(n-((n+1) mod 2)) * A010051(n+((n+1) mod 2)) for n > 2.

a(n) = 1 - (pi(n) - pi(n-2))*(pi(n+1) - pi(n-1)), for n>3, where pi = A000720. - Ridouane Oudra, Jan 10 2022

Extensions

More terms from Antti Karttunen, Jul 02 2018