A273101 Numbers n such that n - 43, n - 1, n + 1, n + 43 are consecutive primes.

7714800, 8126820, 8341260, 8646060, 9200880, 9422970, 13224270, 13597920, 14012460, 14124630, 15305700, 17008680, 17563920, 18830940, 22603740, 22812150, 24576240, 25197300, 26147040, 26196900, 26932950, 27225240, 30305580, 31214640

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 - 43 and n + 1 belong to A272176 (p and p + 44 are primes) and A134120 (p such that p + 42 is the next prime).

The numbers n - 43 and n - 1 belong to A271982 (p and p + 42 are primes).

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Twin Primes

Example

7714800 is the average of the four consecutive primes 7714757, 7714799, 7714801, 7714843.
8126820 is the average of the four consecutive primes 8126777, 8126819, 8126821, 8126863.

Prog

(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 60000001, 6):
..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-43 and nextprime(i+1) == i+43: print (i, end=', ')
(PARI) is(n)=n%30==0 && isprime(n-1) && isprime(n+1) && nextprime(n+2)==n+43 && precprime(n-2)==n-43 \\ Charles R Greathouse IV, May 15 2016

Crossrefs

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

Sequence in context: A192105 A233597 A258954 * A124416 A320516 A319809

Adjacent sequences: A273098 A273099 A273100 * A273102 A273103 A273104

Keyword

nonn

Author

Karl V. Keller, Jr., May 15 2016

Status

approved