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

1,1

Links

Table of n, a(n) for n=1..97.

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000040, A024675.

Sequence in context: A291520 A354445 A317646 * A302981 A205785 A303235

Adjacent sequences: A305745 A305746 A305747 * A305749 A305750 A305751

Keyword

nonn,easy

Author

Dimitris Valianatos, Jun 09 2018

Status

approved