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

1,1

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.

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Twin Primes

Formula

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A014574, A052378, A077800 (twin primes), A256753.

Sequence in context: A338259 A133403 A152615 * A259263 A341039 A279369

Adjacent sequences: A258085 A258086 A258087 * A258089 A258090 A258091

Keyword

nonn

Author

Karl V. Keller, Jr., May 19 2015

Extensions

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

Status

approved