A274042 Numbers k such that k - 53, k - 1, k + 1, k + 53 are consecutive primes.

9401700, 64312710, 78563130, 83494350, 92978310, 101520540, 111105090, 121631580, 136765860, 138330780, 139027950, 145673850, 157008390, 163050090, 166418280, 169288530, 170473410, 177920850, 198963210, 200765250, 213504870, 220428600

Offset: 1

Author

Karl V. Keller, Jr., Jun 07 2016

Keywords

• nonn

Comments

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

The numbers n - 53 and n + 1 belong to A204665 (p such that p + 52 is the next prime).

The numbers n - 53 and n - 1 belong to primes p such that p + 54 is prime.

Examples

			9401700 is the average of the four consecutive primes 9401647, 9401699, 9401701, 9401753.
64312710 is the average of the four consecutive primes 64312657, 64312709, 64312711, 64312763.
		

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

Mathematica

Select[Partition[Prime[Range[122*10^5]],4,1],Differences[#]=={52,2,52}&][[All,2]]+1 (* Harvey P. Dale, Mar 07 2018 *)

Python

from sympy import isprime,prevprime,nextprime
for i in range(0,250000001,6):
  if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-53 and nextprime(i+1) == i+53: print (i,end=', ')