A337489 - OEIS

A337489

a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-1..k+1} prime(j)) sets a new record. A337488 are the corresponding values of k.

%I #6 Aug 30 2020 07:13:34

%S 3,7,29,113,523,1151,1327,9551,15683,19609,25471,31397,156007,360653,

%T 370261,492113,1349533,1357201,1357333,1562051,2010733,4652507,

%U 17051707,17051887,20831323,47326693,47326913,122164747,189695893,191912783,387096133,428045741,436273291

%N a(n) is the k-th prime, such that abs(prime(k) - Sum_{j=k-1..k+1} prime(j)) sets a new record. A337488 are the corresponding values of k.

%e List of first terms:

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

%e 3, 2, 1/3 = (2 + 3 + 5)/3 - 3

%e 7, 4, 2/3 = (5 + 7 + 11)/3 - 7

%e 29, 10, -4/3 = (23 + 29 + 31)/3 - 29

%e 113, 30, 10/3

%e 523, 99, 16/3

%e 1151, 190, -20/3

%e 1327, 217, 28/3

%e 9551, 1183, 32/3

%o (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(500000000)

%Y Cf. A006562, A034961, A075540, A292530, A337438, A337439, A337488.

%K nonn

%O 1,1

%A _Hugo Pfoertner_, Aug 29 2020