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.

3, 7, 29, 113, 523, 1151, 1327, 9551, 15683, 19609, 25471, 31397, 156007, 360653, 370261, 492113, 1349533, 1357201, 1357333, 1562051, 2010733, 4652507, 17051707, 17051887, 20831323, 47326693, 47326913, 122164747, 189695893, 191912783, 387096133, 428045741, 436273291

Offset: 1

Author

Hugo Pfoertner, Aug 29 2020

Keywords

• nonn

Comments

A337488 are the corresponding values of k.

Examples

			List of first terms:
   a(n) pi(a(n))  average-median
     3,      2,   1/3  = (2 + 3 + 5)/3 - 3
     7,      4,   2/3  = (5 + 7 + 11)/3 - 7
    29,     10,  -4/3  = (23 + 29 + 31)/3 - 29
   113,     30,  10/3
   523,     99,  16/3
  1151,    190, -20/3
  1327,    217,  28/3
  9551,   1183,  32/3
		

Crossrefs

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

Programs

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)};
a337489(500000000)

Extensions

Name edited by Peter Munn, Aug 01 2025