A305748 Distance of a prime number from the average of the next two consecutive prime numbers.

2, 3, 4, 5, 4, 5, 4, 7, 7, 5, 8, 5, 4, 7, 9, 7, 5, 8, 5, 5, 8, 7, 10, 10, 5, 4, 5, 4, 11, 16, 7, 7, 7, 11, 5, 9, 8, 7, 9, 7, 7, 11, 4, 5, 8, 18, 14, 5, 4, 7, 7, 7, 13, 9, 9, 7, 5, 8, 5, 7, 17, 16, 5, 4, 11, 17, 11, 11, 4, 7, 10, 11, 9, 8, 7, 10, 10, 8, 13, 11, 7, 11, 5, 8, 7, 10, 10, 5, 4, 10, 16, 10, 8, 10, 7, 12, 13

Offset: 1

Author

Dimitris Valianatos, Jun 09 2018

Keywords

• nonn
• easy

Examples

			For n=4 prime(4) = 7. The next two primes are 11, 13 and the average (11 + 13) / 2 = 12. So 12 - 7 = 5 and a(4) = 5.
		

Crossrefs

Cf. A000040, A024675.

Programs

Mathematica

Map[Mean@ Rest@ # - First@ # &, Partition[Prime@ Range@ 99, 3, 1]] (* Michael De Vlieger, Jun 11 2018 *)

PARI

{ forprime(n = 2, 100,  p1 = nextprime(n+1); p2 = nextprime(p1 + 1);
print1((p1 + p2) / 2 - n", ")) }

Formula

a(n) = A024675(n) - A000040(n).