A273355 Numbers n such that n - 47, n - 1, n + 1, n + 47 are consecutive primes.

15370470, 15462870, 18216510, 23726160, 30637050, 31054740, 38907060, 39220080, 44499900, 44678190, 60563100, 66248550, 86219910, 87095190, 87948780, 93773970, 96802860, 103011990, 105953760, 105978330, 106960410, 111219990, 116281770

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 - 47 and n + 1 belong to A134122 (p such that p + 46 is the next prime).

The numbers n - 47 and n - 1 belong to primes p such that p and p + 48 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

15370470 is the average of the four consecutive primes 15370423, 15370469, 15370471, 15370517.
15462870 is the average of the four consecutive primes 15462823, 15462869, 15462871, 15462917.

Prog

(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 160000001, 6):
..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-47 and nextprime(i+1) == i+47: print (i, end=', ')
(PARI) is(n)=isprime(n-1) && isprime(n+1) && precprime(n-2)==n-47 && nextprime(n+2)==n+47 \\ Charles R Greathouse IV, Jun 08 2016

Crossrefs

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

Sequence in context: A234480 A186616 A128480 * A207797 A186050 A121840

Adjacent sequences: A273352 A273353 A273354 * A273356 A273357 A273358

Keyword

nonn

Author

Karl V. Keller, Jr., May 20 2016

Status

approved