A268305 Numbers n such that n - 37, n - 1, n + 1, n + 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

1,1

Comments

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

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

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

Links

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

Eric Weisstein's World of Mathematics, Twin Primes

Example

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.

Mathematica

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

Prog

(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=', ')

Crossrefs

Cf. A014574, A077800 (twin primes), A249674, A256753.

Sequence in context: A346674 A236154 A126252 * A364701 A236117 A255694

Adjacent sequences: A268302 A268303 A268304 * A268306 A268307 A268308

Keyword

nonn,changed

Author

Karl V. Keller, Jr., Apr 17 2016

Status

approved