A077389 Smallest integer that is the average of n consecutive primes.

2, 4, 5, 9, 79, 12, 17, 30, 261, 30, 49, 23, 71, 51, 29, 31, 37, 39, 125, 56, 95, 52, 38, 133, 157, 113, 353, 70, 347, 89, 111, 139, 179, 187, 281, 124, 137, 95, 347, 100, 153, 105, 491, 273, 185, 177, 377, 199, 599, 1032, 149, 274, 110, 200, 485, 251, 155, 315

Offset

1,1

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

a(n) = A077388(n)/n.

Example

a(5) = 79 because the average of the 5 consecutive primes 71, 73, 79, 83, and 89 is 79, and this is the smallest such set: for example, the average of 7, 11, 13, 17, and 19 is 13.4, which is not an integer.

Mathematica

f[n_] := Block[{k = 1, t}, While[t = Table[Prime[i], {i, k, k + n - 1}]; Mod[Plus @@ t, n] > 0, k++ ]; t]; Mean /@ Table[f[n], {n, 58}] (* Ray Chandler, Oct 09 2006 *)

Prog

(PARI) a(n) = {my(v=primes(n), s=vecsum(v), p=prime(n)); while(s%n, s-=v[1]-p=nextprime(p+1); v=concat(v[2..n], p)); s/n; } \\ Jinyuan Wang, Sep 05 2020

Crossrefs

Cf. A054892, A077388, A082592, A122820.

Sequence in context: A279786 A255515 A067298 * A122991 A245512 A366351

Adjacent sequences: A077386 A077387 A077388 * A077390 A077391 A077392

Keyword

nonn

Author

Amarnath Murthy, Nov 06 2002

Extensions

More terms from Sascha Kurz, Jan 30 2003

Change to definition based on comment by Zak Seidov, Mar 20 2013

Status

approved