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A273356
Numbers n such that n - 49, n - 1, n + 1, n + 49 are consecutive primes.
1
913638, 2763882, 4500492, 6220518, 6473148, 13884468, 15131982, 15729942, 19671930, 20494602, 21372888, 23791350, 25541028, 29535348, 30787788, 30906768, 32085372, 34128168, 34139802, 34550430, 35989980, 37473180, 37784310, 38106372
OFFSET
1,1
COMMENTS
This sequence is a subsequence of A014574 (average of twin prime pairs) and A256753.
The terms ending in 0 belong to A249674 (divisible by 30).
The terms ending in 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.
The numbers n - 49 and n + 1 belong to A134123 (p such that p + 48 is the next prime).
The numbers n - 49 and n - 1 belong to A062284 (p and p + 50 are primes).
LINKS
Eric Weisstein's World of Mathematics, Twin Primes
EXAMPLE
913638 is the average of the four consecutive primes 913589, 913637, 913639, 913687.
2763882 is the average of the four consecutive primes 2763833, 2763881, 2763883, 2763931.
MATHEMATICA
Mean/@Select[Partition[Prime[Range[2325200]], 4, 1], Differences[#]=={48, 2, 48}&] (* Harvey P. Dale, Feb 10 2024 *)
PROG
(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 60000001, 6):
..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-49 and nextprime(i+1) == i+49: print (i, end=', ')
(PARI) is(n)=isprime(n-1) && isprime(n+1) && precprime(n-2)==n-49 && nextprime(n+2)==n+49 \\ Charles R Greathouse IV, Jun 08 2016
CROSSREFS
Cf. A014574, A077800 (twin primes), A249674, A256753.
Sequence in context: A236617 A237155 A112688 * A253991 A253998 A258908
KEYWORD
nonn
AUTHOR
Karl V. Keller, Jr., May 20 2016
STATUS
approved