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

Author

Jean-Marc Rebert, Jul 12 2023

Keywords

• sign

Examples

			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.
		

Links

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

Crossrefs

Cf. A000720, A082080, A363168.

Programs

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 *)

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

Formula

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