A259025 Numbers k such that k is the average of four consecutive primes k-11, k-1, k+1 and k+11.

420, 1050, 2028, 2730, 3582, 4230, 4242, 4272, 4338, 6090, 6132, 6690, 6792, 8220, 11058, 11160, 11970, 12252, 15288, 19542, 19698, 21588, 21600, 26892, 27540, 28098, 28308, 29400, 30840, 30870, 31080, 32412, 42072, 45318, 47808, 48120

Offset: 1

Author

Karl V. Keller, Jr., Jun 16 2015

Keywords

• nonn

Comments

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

The terms ending in 0 are congruent to 0 mod 30.

The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.

Examples

			For n=420: 409, 419, 421, 431 are consecutive primes (n-11=409, n-1=419, n+1=421, n+11=431).
For n=1050: 1039, 1049, 1051, 1061 are consecutive primes (n-11=1039, n-1=1049, n+1=1051, n+11=1061).
		

Links

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

Crossrefs

Cf. A052376, A077800 (twin primes), A014574, A249674 (30n), A256753.

Programs

Mathematica

{p, q, r, s} = {2, 3, 5, 7}; lst = {}; While[p < 50000, If[ Differences[{p, q, r, s}] == {10, 2, 10}, AppendTo[lst, q + 1]]; {p, q, r, s} = {q, r, s, NextPrime@ s}]; lst (* Robert G. Wilson v, Jul 15 2015 *)
Mean/@Select[Partition[Prime[Range[5000]],4,1],Differences[#]=={10,2,10}&] (* Harvey P. Dale, Sep 11 2019 *)

PARI

is(n)=n%6==0&&isprime(n-11)&&isprime(n-1)&&isprime(n+1)&&isprime(n+11)&&!isprime(n-7)&&!isprime(n-5)&&!isprime(n+5)&&!isprime(n+7) \\ Charles R Greathouse IV, Jul 17 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-11 and nextprime(i+1) == i+11 :  print (i,end=', ')

Formula

a(n) = A052376(n) + 11. - Robert G. Wilson v, Jul 15 2015