A268305 Numbers k such that k - 37, k - 1, k + 1, k + 37 are consecutive primes.

1524180, 3264930, 3970530, 5438310, 5642910, 6764940, 8176410, 10040880, 10413900, 10894320, 11639520, 12352980, 13556340, 15900720, 16897590, 17283360, 18168150, 18209100, 18686910, 19340220, 20099940, 20359020, 20483340, 21028290, 21846360

Offset: 1

Author

Karl V. Keller, Jr., Apr 17 2016

Keywords

• nonn

Comments

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

The numbers k - 37 and k + 1 belong to A156104 (p and p + 36 are primes) and A134117 (p where p + 36 is the next prime).

The numbers k - 37 and k - 1 belong to A271347 (p and p + 38 are primes).

Examples

			1524180 is the average of the four consecutive primes 1524143, 1524179, 1524181, 1524217.
3264930 is the average of the four consecutive primes 3264893, 3264929, 3264931, 3264967.
		

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[14*10^5]],4,1],Differences[#]=={36,2,36}&][[All,2]]+1 (* Harvey P. Dale, Mar 12 2018 *)

Python

from sympy import isprime,prevprime,nextprime
for i in range(0,30000001,6):
  if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-37 and nextprime(i+1) == i+37 : print (i,end=', ')