login
a(n) = smallest prime number p which is the arithmetic mean of n-th prime < p and n-th prime > p.
5

%I #9 Oct 10 2019 13:57:05

%S 5,11,11,41,29,37,53,67,131,71,97,139,127,727,193,157,191,211,191,359,

%T 307,521,349,577,571,353,307,487,347,541,571,487,541,409,947,593,563,

%U 569,787,547,587,983,587,569,587,1223,563,557,1213,569,563,1381,1213

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

%H Hans Havermann, <a href="/A126243/b126243.txt">Table of n, a(n) for n = 1..10000.</a>

%H Hans Havermann, <a href="/A126243/a126243pj.jpg">Plot of n, a(n) for n = 1..10000</a>

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

%t 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 *)

%Y Cf. A006562, A119381, A126238-A126243.

%K nonn

%O 1,1

%A _Artur Jasinski_, Dec 21 2006

%E Extended by _Ray Chandler_, Dec 27 2006

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