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A273355
Numbers n such that n - 47, n - 1, n + 1, n + 47 are consecutive primes.
1
15370470, 15462870, 18216510, 23726160, 30637050, 31054740, 38907060, 39220080, 44499900, 44678190, 60563100, 66248550, 86219910, 87095190, 87948780, 93773970, 96802860, 103011990, 105953760, 105978330, 106960410, 111219990, 116281770
OFFSET
1,1
COMMENTS
This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
The numbers n - 47 and n + 1 belong to A134122 (p such that p + 46 is the next prime).
The numbers n - 47 and n - 1 belong to primes p such that p and p + 48 are primes.
LINKS
Eric Weisstein's World of Mathematics, Twin Primes
EXAMPLE
15370470 is the average of the four consecutive primes 15370423, 15370469, 15370471, 15370517.
15462870 is the average of the four consecutive primes 15462823, 15462869, 15462871, 15462917.
PROG
(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 160000001, 6):
..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-47 and nextprime(i+1) == i+47: print (i, end=', ')
(PARI) is(n)=isprime(n-1) && isprime(n+1) && precprime(n-2)==n-47 && nextprime(n+2)==n+47 \\ Charles R Greathouse IV, Jun 08 2016
CROSSREFS
Cf. A014574, A077800 (twin primes), A249674, A256753.
Sequence in context: A234480 A186616 A128480 * A207797 A186050 A121840
KEYWORD
nonn
AUTHOR
Karl V. Keller, Jr., May 20 2016
STATUS
approved