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A270754
Numbers n such that n - 31, n - 1, n + 1 and n + 31 are consecutive primes.
1
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
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
KEYWORD
nonn
AUTHOR
Karl V. Keller, Jr., Mar 22 2016
STATUS
approved