OFFSET
1,1
COMMENTS
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-29 and n+1 belong to A252090 (p and p+28 are primes) and A124595 (p where p+28 is the next prime).
The numbers n-29 and n-1 belong to A049481 (p and p+30 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
14592 is the average of the four consecutive primes 14563, 14591, 14593, 14621.
84348 is the average of the four consecutive primes 84319, 84347, 84349, 84377.
MATHEMATICA
Select[Prime@Range@100000, NextPrime[#, {1, 2, 3}] == {28, 30, 58} + # &] + 29 (* Vincenzo Librandi, Dec 12 2015 *)
Mean/@Select[Partition[Prime[Range[125000]], 4, 1], Differences[#]=={28, 2, 28}&] (* Harvey P. Dale, May 02 2016 *)
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-29 and nextprime(i+1) == i+29 : print (i, end=', ')
CROSSREFS
KEYWORD
nonn
AUTHOR
Karl V. Keller, Jr., Dec 11 2015
STATUS
approved