A271323 Numbers n such that n - 41, n - 1, n + 1, n + 41 are consecutive primes.

383220, 1269642, 1528938, 2590770, 3014700, 3158298, 3697362, 3946338, 4017312, 4045050, 4545642, 4711740, 4851618, 4871568, 5141178, 5194602, 5925042, 5972958, 5990820, 6075030, 6179862, 6212202, 6350760, 6442938, 6549312, 6910638, 6912132

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) and A256753.

The terms ending in 0 belong to A249674 (divisible by 30).

The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.

The numbers n - 40 and n + 1 belong to A126721 (p such that p + 40 is the next prime) and A271981 (p and p + 40 are primes).

The numbers n - 40 and n - 1 belong to A271982 (p and p + 42 are primes).

Examples

			383220 is the average of the four consecutive primes 383179, 383219, 383221, 383261.
1269642 is the average of the four consecutive primes 1269601, 1269641, 1269643, 1269683.
		

Links

• Karl V. Keller, Jr., 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

Mathematica

Mean/@Select[Partition[Prime[Range[472000]],4,1],Differences[#] == {40,2,40}&] (* Harvey P. Dale, Oct 16 2021 *)

Python

from sympy import isprime,prevprime,nextprime
for i in range(0,12000001,6):
  if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-41 and nextprime(i+1) == i+41: print (i,end=', ')