A329273 a(1)=1. If n is prime, a(n)=0; if not, a(n) = (the smallest prime number greater than n) minus (the largest prime number smaller than n) minus 1.

1, 0, 0, 1, 0, 1, 0, 3, 3, 3, 0, 1, 0, 3, 3, 3, 0, 1, 0, 3, 3, 3, 0, 5, 5, 5, 5, 5, 0, 1, 0, 5, 5, 5, 5, 5, 0, 3, 3, 3, 0, 1, 0, 3, 3, 3, 0, 5, 5, 5, 5, 5, 0, 5, 5, 5, 5, 5, 0, 1, 0, 5, 5, 5, 5, 5, 0, 3, 3, 3, 0, 1, 0, 5, 5, 5, 5, 5, 0, 3, 3, 3, 0, 5, 5, 5, 5, 5, 0, 7, 7, 7, 7, 7, 7, 7, 0, 3, 3, 3

Offset: 1

Author

Todor Szimeonov, Nov 11 2019

Keywords

• nonn

Comments

When n is not a prime number, a(n) expresses the size of the prime gap to which n belongs.

Examples

			Let n=9. The smallest prime number, greater than 9 is 11, the largest prime number, smaller than 9 is 7. a(9)=11-7-1=3.
		

Crossrefs

Cf. A072680, A151799, A151800.

Programs

Mathematica

Array[Which[# == 1, 1, PrimeQ@ #, 0, True, Prime[# + 1] - Prime@ # - 1 &@ PrimePi@ #] &, 105] (* Michael De Vlieger, Nov 18 2019 *)

PARI

a(n) = if (n==1, 1, if (isprime(n), 0, nextprime(n+1) - precprime(n-1) - 1)); \\ Michel Marcus, Dec 01 2019

Formula

a(1)=1. If n is prime, a(n)=0; if not, a(n) = nextprime(n) - precprime(n) - 1.

The nonzero terms are one less than the nonzero terms of A072680. More precisely, a(n) = A072680(n) - sign(A072680(n)) for n > 1. - Rémy Sigrist, Nov 30 2019