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

Author

Karl V. Keller, Jr., May 15 2016

Keywords

• nonn

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).

Examples

			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.
		

Links

• Charles R Greathouse IV, 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

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

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=', ')