A100820 Number of odd numbers between prime(n) and prime(n+1).

0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 2, 1, 0, 1, 2, 2, 0, 2, 1, 0, 2, 1, 2, 3, 1, 0, 1, 0, 1, 6, 1, 2, 0, 4, 0, 2, 2, 1, 2, 2, 0, 4, 0, 1, 0, 5, 5, 1, 0, 1, 2, 0, 4, 2, 2, 2, 0, 2, 1, 0, 4, 6, 1, 0, 1, 6, 2, 4, 0, 1, 2, 3, 2, 2, 1, 2, 3, 1, 3, 4, 0, 4, 0, 2, 1, 2, 3, 1, 0, 1, 5, 3, 1, 3, 1, 2, 5, 0, 8, 2, 4, 2, 2, 0, 2

Offset: 1

Author

Giovanni Teofilatto, Jan 06 2005

Keywords

• easy
• nonn

Examples

			a(2)=0 because between 3 and 5 there are no odd numbers.
a(3)=0 because between 5 and 7 there are no odd numbers.
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000040, A001223, A028334, A036263.

Programs

Magma

[0] cat [(NthPrime(n+1)-NthPrime(n))/2-1 : n in [2..100]]; // Wesley Ivan Hurt, Jun 01 2016

Maple

P:= select(isprime,[seq(i,i=3..1000,2)]):
0,op(map(`-`,1/2*(P[2..-1]-P[1..-2]),1)); # Robert Israel, Jun 01 2016

Mathematica

Table[Floor[Max[(Prime[n + 1] - Prime[n])/2 - 1, 0] ], {n, 120}] (* Ray Chandler, Jan 09 2005 *)

Formula

a(n) = (prime(n+1)-prime(n))/2-1 = A001223(n)/2-1 for n>=2. - Robert Israel, Jun 01 2016

a(n) = A028334(n) - 1 for n>=2. - Michel Marcus, Jan 04 2023

Extensions

Corrected and extended by Ray Chandler, Jan 09 2005