A364163 Least number k such that average of {prime(i) | k - n <= i <= k + n} is prime(k), or -1 if no such number exists.

1, 3, 22, 7, 94, 16, 20, 10, 12, 166, 727, 40, 37, 71, 702, 56, 41, 76, 33, 424, 314, 133, 71, 726, 241, 35, 618, 205, 78, 138, 1096, 1096, 111, 49, 512, 2006, 5790, 504, 2634, 1497, 199, 1344, 181, 2404, 2237, 162, 241, 470, 667, 81, 106, 2940, 209, 209, 5549

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Formula

a(n) = A000720(A082080(n)). - Michel Marcus, Jul 12 2023

Example

a(0) = 1, because 2/1 = 2 = prime(1), and no lesser number satisfies this.
a(1) = 3, because (3+5+7)/3 = 5 = prime(3), and no lesser number satisfies this.

Mathematica

a[n_] := Module[{ps = Prime[Range[2*n+1]], k = n+1}, While[Total[ps] != (2*n+1)* ps[[n+1]], ps = Join[Rest[ps], {NextPrime[ps[[-1]]]}]; k++]; k]; Array[a, 55, 0] (* Amiram Eldar, Sep 07 2024 *)

Prog

(PARI) a(n) = my(k=n+1); while(sum(i=k-n, k+n, prime(i)) != (2*n+1)*prime(k), k++); k; \\ Michel Marcus, Jul 12 2023

Crossrefs

Cf. A000720, A082080, A363168.

Sequence in context: A161377 A122495 A100977 * A037101 A226028 A248626

Adjacent sequences: A364160 A364161 A364162 * A364164 A364165 A364166

Keyword

sign

Author

Jean-Marc Rebert, Jul 12 2023

Status

approved