%I #7 Aug 30 2020 07:13:19

%S 5,7,19,47,97,109,113,199,887,1151,1277,1327,9551,11777,14143,15727,

%T 19609,25471,31397,156007,360653,370261,492113,1357201,1357333,

%U 1562051,2010733,4652507,17051887,20831323,47326693,47326913,122164747,189695893,428045741,436273291,1453168433

%N a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-2..k+2} prime(j)) sets a new record. A337438 are the corresponding values of k.

%e List of first terms:

%e a(n) pi(a(n)) average-median

%e 5, 3, 3/5 = (2 + 3 + 5 + 7 + 11)/5 - 5

%e 7, 4, 4/5 = (3 + 5 + 7 + 11 + 13)/5 - 7

%e 19, 8, 6/5 = (13 + 17 + 19 + 23 + 29)/5 - 19

%e 47, 15, 8/5

%e 97, 25, -12/5

%e 109, 29, 14/5

%e 113, 30, 22/5

%e 199, 46, 28/5

%e 887, 154, 34/5

%e 1151, 190, -36/5

%e 1277, 206, -38/5

%e 1327, 217, 12

%e 9551, 1183, 14

%o (PARI) a337439(limp) = {my(p1=0,p2=2,p3=3,p4=5,p5=7,s=p1+p2+p3+p4+p5,d=0);forprime(p=11,limp, s=s-p1+p; my(dd=abs(s/5-p4)); if(dd>d,print1(p4,", ");d=dd); p1=p2;p2=p3;p3=p4;p4=p5;p5=p)};

%o a337439(500000000)

%Y Cf. A034964, A337438, A337488, A337489.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Aug 29 2020