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

0,1

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

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

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}]

Prog

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

Crossrefs

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

Sequence in context: A279329 A359430 A374121 * A244525 A214263 A263428

Adjacent sequences: A292435 A292436 A292437 * A292439 A292440 A292441

Keyword

nonn

Author

Wesley Ivan Hurt, Mar 31 2018

Extensions

More terms from Antti Karttunen, Jul 02 2018

Status

approved