A332094 Numerator of the average distance among first n primes.

1, 2, 17, 22, 27, 142, 31, 9, 97, 666, 83, 604, 1529, 1906, 791, 367, 3533, 4238, 5019, 584, 617, 7822, 8995, 518, 473, 13342, 1663, 8324, 3689, 20662, 23003, 532, 1655, 31074, 541, 6218, 2145, 44354, 48187, 2613, 18805, 20330, 65651, 356, 15083, 80894, 28979, 23293

Offset: 2

Author

Andres Cicuttin, Nov 20 2020

Keywords

• nonn
• frac

Crossrefs

Cf. A336814 (denominator), A338869, A339022, A062020.

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}]//Numerator

PARI

lista(nn) = {my(vp = primes(nn)); vector(nn-1, k, k++; numerator((2/(k*(k-1))*sum(j=2, k, sum(i=1, j-1, vp[j] - vp[i])))));} \\ Michel Marcus, Nov 21 2020

Formula

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