A258879 Numbers k such that k is the average of four consecutive primes k-7, k-1, k+1 and k+7.

30, 60, 270, 570, 600, 1230, 1290, 1620, 2340, 2550, 3540, 4020, 4650, 5850, 6270, 6360, 6570, 10860, 11490, 14550, 15270, 17490, 19080, 19380, 19470, 23670, 26730, 29130, 32370, 34260, 41610, 48480, 49200, 49530, 51420, 51480

Offset: 1

Author

Karl V. Keller, Jr., Jun 13 2015

Keywords

• nonn

Comments

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

Examples

			For k=30: 23, 29, 31, 37 are consecutive primes (k-7=23, k-1=29, k+1=31, k+7=37).
For k=60: 53, 59, 61, 67 are consecutive primes (k-7=53, k-1=59, k+1=61, k+7=67).
		

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), A078854, A249674, A256753.

Programs

Magma

[n: n in [13..2*10^5] | IsPrime(n-7) and IsPrime(n-1) and IsPrime(n+1) and IsPrime(n+7)]; // Vincenzo Librandi Jul 16 2015

Mathematica

Select[ 5 Range@ 11000, PrimeQ[# - 7] && PrimeQ[# - 1] && PrimeQ[# + 1] && PrimeQ[# + 7] &] (* Robert G. Wilson v, Jun 28 2015 *)

PARI

main(size)={my(v=vector(size),i,t=8);for(i=1,size,while(1,if(isprime(t-7)&&isprime(t-1)&&isprime(t+1)&&isprime(t+7),v[i]=t;break,t++));t++);return(v);} /* Anders Hellström, Jul 17 2015 */

Python

from sympy import isprime, prevprime, nextprime
for i in range(0, 10001, 2):
  if isprime(i-1) and isprime(i+1):
    if prevprime(i-1) == i-7 and nextprime(i+1) == i+7: print(i, end=', ')

Formula

a(n) = A078854(n) + 7.