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A262668
Numbers n such that n-19, n-1, n+1 and n+19 are consecutive primes.
1
20982, 28182, 51768, 57222, 76422, 87720, 90678, 104850, 108108, 110730, 141180, 199602, 227112, 248118, 264600, 268842, 304392, 304458, 320082, 322920, 330018, 382728, 401670, 414432, 429972, 450258, 467082, 489408, 520548, 535608, 540120
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.
LINKS
Eric Weisstein's World of Mathematics, Twin Primes
EXAMPLE
20982 is the average of the four consecutive primes 20963, 20981, 20983, 21001.
28182 is the average of the four consecutive primes 28163, 28181, 28183, 28201.
MATHEMATICA
Select[Range[6, 600000, 6], And[AllTrue[{# - 1, # + 1}, PrimeQ], NextPrime[# - 1, -1] == # - 19, NextPrime[# + 1] == # + 19] &] (* Michael De Vlieger, Sep 27 2015, Version 10 *)
Select[Prime@Range@60000, NextPrime[#, {1, 2, 3}] == {18, 20, 38} + # &] + 19 (* Vincenzo Librandi, Oct 10 2015 *)
Mean/@Select[Partition[Prime[Range[50000]], 4, 1], Differences[#]=={18, 2, 18}&] (* Harvey P. Dale, Jan 16 2019 *)
PROG
(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 1000001, 6):
..if isprime(i-1) and isprime(i+1):
....if prevprime(i-1) == i-19 and nextprime(i+1) == i+19 : print(i, end=', ')
CROSSREFS
Cf. A014574, A077800 (twin primes), A249674, A256753.
Sequence in context: A188104 A278903 A233649 * A344354 A344355 A231314
KEYWORD
nonn
AUTHOR
Karl V. Keller, Jr., Sep 26 2015
STATUS
approved