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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
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
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
KEYWORD
sign
AUTHOR
Jean-Marc Rebert, Jul 12 2023
STATUS
approved