

A077389


Smallest integer that is the average of n consecutive primes.


7



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
(list;
graph;
refs;
listen;
history;
text;
internal format)



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 A232616
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



