A082592 -id:A082592 - cp's OEIS frontend

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

Amarnath Murthy, Nov 06 2002

nonn

			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.

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

Cf. A054892, A077388, A082592, A122820.

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 *)

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

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

More terms from Sascha Kurz, Jan 30 2003

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

A122820 Array read by rows in which n-th row contains n successive primes with least sum divisible by n.

Original entry on oeis.org

2, 3, 5, 3, 5, 7, 5, 7, 11, 13, 71, 73, 79, 83, 89, 5, 7, 11, 13, 17, 19, 7, 11, 13, 17, 19, 23, 29, 17, 19, 23, 29, 31, 37, 41, 43, 239, 241, 251, 257, 263, 269, 271, 277, 281, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 5, 7, 11, 13, 17

Offset: 1

Ray Chandler, Sep 27 2006

			Triangle begins:
2
3 5
3 5 7
5 7 11 13
71 73 79 83 89
5 7 11 13 17 19
7 11 13 17 19 23 29
17 19 23 29 31 37 41 43
239 241 251 257 263 269 271 277 281
13 17 19 23 29 31 37 41 43 47
29 31 37 41 43 47 53 59 61 67 71
5 7 11 13 17 19 23 29 31 37 41 43

Cf. A054892 (first term of each row), A077388 (row sum), A077389 (row average).

Cf. A082592, A082596, A082638, A082653, A082661.

f[n_] := Block[{k = 1, t},While[t = Table[Prime[i], {i, k, k + n - 1}]; Mod[Plus @@ t, n] > 0, k++ ];t];Flatten[Table[f[n], {n, 12}]]

A082653 For smallest numbers k such that A082596(k) = n, sequence gives A060863(k).

Original entry on oeis.org

2, 30, 910, 15203

Offset: 1

Naohiro Nomoto, May 17 2003

			For n=2; smallest number k = 20, A082596(20) = 2. so a(2) = A060863(20) = 30.

Cf. A060863, A077389, A082592.

cp's OEIS Frontend

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

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A122820 Array read by rows in which n-th row contains n successive primes with least sum divisible by n.

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Mathematica

A082653 For smallest numbers k such that A082596(k) = n, sequence gives A060863(k).

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