A126243 a(n) = smallest prime number p which is the arithmetic mean of n-th prime < p and n-th prime > p.

5, 11, 11, 41, 29, 37, 53, 67, 131, 71, 97, 139, 127, 727, 193, 157, 191, 211, 191, 359, 307, 521, 349, 577, 571, 353, 307, 487, 347, 541, 571, 487, 541, 409, 947, 593, 563, 569, 787, 547, 587, 983, 587, 569, 587, 1223, 563, 557, 1213, 569, 563, 1381, 1213

Offset: 1

Author

Artur Jasinski, Dec 21 2006

Keywords

• nonn

Examples

			5 is the smallest prime p = prime(n) such that p = (prime(n-1)+prime(n+1))/2 (5 = (3+7)/2).
		

Links

• Hans Havermann, Table of n, a(n) for n = 1..10000.
• Hans Havermann, Plot of n, a(n) for n = 1..10000

Crossrefs

Cf. A006562, A119381, A126238-A126243.

Programs

Mathematica

f[n_] := Block[{k = n + 1, p},While[p = (Prime[k - n] + Prime[k + n])/2; p != Prime[k], k++ ];p];Table[f[n], {n, 58}] (* Ray Chandler, Dec 27 2006 *)

Extensions

Extended by Ray Chandler, Dec 27 2006

Figure and b-file updated by Hans Havermann, Feb 07 2007