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

1,1

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).

Links

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

Eric Weisstein's World of Mathematics, Twin Primes

Example

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.

Mathematica

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

Prog

(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=', ')

Crossrefs

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

Sequence in context: A295454 A273772 A206365 * A205759 A205589 A157843

Adjacent sequences: A271320 A271321 A271322 * A271324 A271325 A271326

Keyword

nonn,changed

Author

Karl V. Keller, Jr., May 15 2016

Status

approved