A274042 Numbers n such that n - 53, n - 1, n + 1, n + 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

1,1

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.

Links

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

Eric Weisstein's World of Mathematics, Twin Primes

Example

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.

Mathematica

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

Prog

(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=', ')

Crossrefs

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

Sequence in context: A328207 A069376 A281570 * A066703 A270994 A162030

Adjacent sequences: A274039 A274040 A274041 * A274043 A274044 A274045

Keyword

nonn

Author

Karl V. Keller, Jr., Jun 07 2016

Status

approved