A258088 Numbers n such that n is the average of four consecutive primes n-5, n-1, n+1 and n+5.

12, 18, 42, 102, 108, 228, 312, 462, 858, 882, 1092, 1302, 1428, 1488, 1872, 1998, 2688, 3462, 4518, 4788, 5232, 5652, 6828, 7878, 8292, 10458, 13692, 13878, 15732, 16062, 16068, 16188, 17388, 19422, 19428, 20748, 21018, 21318, 22278, 23058

Offset: 1

Author

Karl V. Keller, Jr., May 19 2015

Keywords

• nonn

Comments

Previous name was: Numbers n such that n is the average of some twin prime pair p, q (q=p+2) (i.e., n=p+1=q-1) where p-4, p, q, and q+4 are consecutive primes.

This is a subsequence of A014574 (average of twin prime pairs) and A256753.

Examples

			12 is the average of the four consecutive primes 7, 11, 13, 17.
18 is the average of the four consecutive primes 13, 17, 19, 23.
		

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, A052378, A077800 (twin primes), A256753.

Programs

Mathematica

a={};Do[If[Prime[x + 3] - Prime[x]==10, AppendTo[a, Prime[x]+ 5]], {x, 1, 4000}]; a (* Vincenzo Librandi, Jul 18 2015 *)
Mean/@Select[Partition[Prime[Range[3000]],4,1],Differences[#]=={4,2,4}&] (* Harvey P. Dale, Sep 18 2018 *)

PARI

is(n)=isprime(n-5)&&isprime(n-1)&&isprime(n+1)&&isprime(n+5) \\ Charles R Greathouse IV, Aug 28 2015

Python

from sympy import isprime,prevprime,nextprime
for i in range(0,50001,2):
  if isprime(i-1) and isprime(i+1):
    if prevprime(i-1) == i-5 and nextprime(i+1) == i+5: print (i,end=', ')

Formula

a(n) = A052378(n) + 5. - Karl V. Keller, Jr., Jul 17 2015

Extensions

New name from Karl V. Keller, Jr., Jul 21 2015