A051795 Doubly balanced primes: primes which are averages of both their immediate and their second neighbors.

18731, 25621, 28069, 30059, 31051, 44741, 76913, 97441, 103669, 106681, 118831, 128449, 135089, 182549, 202999, 240491, 245771, 249199, 267569, 295387, 347329, 372751, 381401, 435751, 451337, 455419, 471521, 478099, 498301, 516877, 526441, 575231, 577873

Offset: 1

Author

Harvey P. Dale, Dec 10 1999

Keywords

• easy
• nonn

Comments

Could also be called overbalanced or [3,5]-balanced primes: balanced primes which are equally average of 3,5 consecutive prime neighbors as follows: a(n)=[q+a(n)+r]/3=[p+q+a(n)+r+s]/5 See 3-balanced=A006562;[3,5,7]-balanced=A081415. - Labos Elemer, Apr 02 2003

Numbers m such that A346399(m) is odd and >= 5. - Ya-Ping Lu, May 11 2024

Examples

			25621 belongs to the sequence because 25621 = (25609 + 25633)/2 = (25603 + 25609 + 25633 + 25639)/4.
		

Links

• Jud McCranie and Sebastian Petzelberger, Table of n, a(n) for n = 1..10000 (first 1000 terms from Jud McCranie)

Crossrefs

Cf. A006562, A081415, A096710, A055380, A346399.

Programs

Mathematica

Transpose[Select[Partition[Prime[Range[50000]],5,1],(#[[1]]+#[[5]])/2 == (#[[2]]+#[[4]])/2 == #[[3]]&]][[3]] (* Harvey P. Dale, Sep 13 2013 *)

Python

from sympy import nextprime; p, q, r, s, t = 2, 3, 5, 7, 11
while t < 580000:
    if p + t == q + s == 2*r: print(r, end = ', ')
    p, q, r, s, t = q, r, s, t, nextprime(t) # Ya-Ping Lu, May 11 2024