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A337489 a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-1..k+1} prime(j)/3) sets a new record.

%I A337489 #10 Aug 01 2025 07:48:07
%S A337489 3,7,29,113,523,1151,1327,9551,15683,19609,25471,31397,156007,360653,
%T A337489 370261,492113,1349533,1357201,1357333,1562051,2010733,4652507,
%U A337489 17051707,17051887,20831323,47326693,47326913,122164747,189695893,191912783,387096133,428045741,436273291
%N A337489 a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-1..k+1} prime(j)/3) sets a new record.
%C A337489 A337488 are the corresponding values of k.
%e A337489 List of first terms:
%e A337489    a(n) pi(a(n))  average-median
%e A337489      3,      2,   1/3  = (2 + 3 + 5)/3 - 3
%e A337489      7,      4,   2/3  = (5 + 7 + 11)/3 - 7
%e A337489     29,     10,  -4/3  = (23 + 29 + 31)/3 - 29
%e A337489    113,     30,  10/3
%e A337489    523,     99,  16/3
%e A337489   1151,    190, -20/3
%e A337489   1327,    217,  28/3
%e A337489   9551,   1183,  32/3
%o A337489 (PARI) a337489(limp) = {my(p1=0, p2=2, p3=3, s=p1+p2+p3, d=0); forprime(p=5, limp, s=s-p1+p; my(dd=abs(s/3-p3)); if(dd>d, print1(p3, ", "); d=dd); p1=p2; p2=p3; p3=p)};
%o A337489 a337489(500000000)
%Y A337489 Cf. A006562, A034961, A075540, A292530, A337438, A337439, A337488.
%K A337489 nonn
%O A337489 1,1
%A A337489 _Hugo Pfoertner_, Aug 29 2020
%E A337489 Name edited by _Peter Munn_, Aug 01 2025