A260959 Numbers n such that n is the average of four consecutive primes n-13, n-1, n+1 and n+13.

7950, 10500, 32970, 33330, 34470, 36900, 43050, 66360, 71550, 74610, 87120, 89070, 92400, 94560, 95190, 102000, 104310, 121950, 125790, 133980, 148470, 156900, 160710, 168630, 174930, 182640, 194070, 204600, 206250, 230340, 244380, 246510

Offset: 1

Author

Karl V. Keller, Jr., Aug 06 2015

Keywords

• nonn

Comments

This is a subsequence of A014574 (average of twin prime pairs), A256753 and A249674 (30n).

Examples

			7950 is the average of the four consecutive primes 7937, 7949, 7951, 7963.
10500 is the average of the four consecutive primes 10487, 10499, 10501, 10513.
		

Links

• Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Twin Primes

Crossrefs

Cf. A014574, A077800 (twin primes), A249674, A256753.

Programs

Perl

use ntheory ":all"; say join ", ", map { $+1 } grep { next_prime($+2)-$==14 } grep { $-prev_prime($)==12 } @{twin_primes(1e6)}; # _Dana Jacobsen, Oct 03 2015

Python

from sympy import isprime,prevprime,nextprime
for i in range(0,300001,2):
   if isprime(i-1) and isprime(i+1):
    if prevprime(i-1) == i-13 and nextprime(i+1) == i+13 :  print (i,end=', ')