A270754 Numbers n such that n - 31, n - 1, n + 1 and n + 31 are consecutive primes.

90438, 258918, 293862, 385740, 426162, 532950, 1073952, 1317192, 1318410, 1401318, 1565382, 1894338, 1986168, 2174772, 2612790, 2764788, 3390900, 3450048, 3618960, 3797250, 3961722, 3973062, 4074870, 4306230, 4648068, 4917360, 5351010, 5460492

Offset

1,1

Comments

This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.

The terms ending in 0 are divisible by 30 (cf. A249674).

The terms ending in 2 and 8 are congruent to 12 mod 30 and 18 mod 30 respectively.

The numbers n - 31 and n + 1 belong to A049481 (p and p + 30 are primes) and A124596 (p where p + 30 is the next prime).

The numbers n - 31 and n - 1 belong to A049489 (p and p + 32 are primes).

Links

Karl V. Keller, Jr., Table of n, a(n) for n = 1..100000

Eric Weisstein's World of Mathematics, Twin Primes

Example

90438 is the average of the four consecutive primes 90407, 90437, 90439, 90469.
258918 is the average of the four consecutive primes 258887, 258917, 258919, 258949.

Prog

(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 1000001, 6):
.. if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-31 and nextprime(i+1) == i+31 :  print (i, end=', ')

Crossrefs

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

Sequence in context: A359291 A236908 A331354 * A252915 A075007 A287383

Adjacent sequences: A270751 A270752 A270753 * A270755 A270756 A270757

Keyword

nonn

Author

Karl V. Keller, Jr., Mar 22 2016

Status

approved