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A337439 a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-2..k+2} prime(j)/5) sets a new record.

%I A337439 #12 Aug 01 2025 07:48:04
%S A337439 5,7,19,47,97,109,113,199,887,1151,1277,1327,9551,11777,14143,15727,
%T A337439 19609,25471,31397,156007,360653,370261,492113,1357201,1357333,
%U A337439 1562051,2010733,4652507,17051887,20831323,47326693,47326913,122164747,189695893,428045741,436273291,1453168433
%N A337439 a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-2..k+2} prime(j)/5) sets a new record.
%C A337439 A337438 are the corresponding values of k.
%e A337439 List of first terms:
%e A337439    a(n)  pi(a(n))  average-median
%e A337439      5,      3,     3/5  = (2 + 3 + 5 + 7 + 11)/5 - 5
%e A337439      7,      4,     4/5 = (3 + 5 + 7 + 11 + 13)/5 - 7
%e A337439     19,      8,     6/5 = (13 + 17 + 19 + 23 + 29)/5 - 19
%e A337439     47,     15,     8/5
%e A337439     97,     25,   -12/5
%e A337439    109,     29,    14/5
%e A337439    113,     30,    22/5
%e A337439    199,     46,    28/5
%e A337439    887,    154,    34/5
%e A337439   1151,    190,   -36/5
%e A337439   1277,    206,   -38/5
%e A337439   1327,    217,    12
%e A337439   9551,   1183,    14
%o A337439 (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 a337439(500000000)
%Y A337439 Cf. A034964, A337438, A337488, A337489.
%K A337439 nonn
%O A337439 1,1
%A A337439 _Hugo Pfoertner_, Aug 29 2020
%E A337439 Name edited by _Peter Munn_, Aug 01 2025