A339022 a(n) is the floor of the average distance among first n primes.

1, 2, 2, 4, 5, 6, 7, 9, 10, 12, 13, 15, 16, 18, 19, 21, 23, 24, 26, 27, 29, 30, 32, 34, 36, 38, 39, 41, 42, 44, 46, 48, 50, 52, 54, 56, 57, 59, 61, 63, 65, 67, 69, 71, 72, 74, 77, 79, 81, 83, 85, 86, 88, 90, 92, 95, 96, 98, 100, 102, 104, 106, 108

Offset: 2

Author

Andres Cicuttin, Nov 19 2020

Keywords

• nonn

Comments

Is the limit of a(n)/n finite?

Crossrefs

Cf. A338869 (Shortest most frequent distance among first n primes).

Programs

Mathematica

nmax=64;
Table[Total[Flatten[Table[Table[Prime[k] - Prime[j], {j, 1, k - 1}], {k, 2, n}]]]/(n*(n - 1)/2), {n, 2, nmax}]//Floor

Formula

a(n) = floor((2/(n*(n-1)))*Sum_{j=2..n} Sum_{i=1..j-1} (prime(j) - prime(i))).