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A268305
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Numbers n such that n - 37, n - 1, n + 1, n + 37 are consecutive primes.
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1
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1524180, 3264930, 3970530, 5438310, 5642910, 6764940, 8176410, 10040880, 10413900, 10894320, 11639520, 12352980, 13556340, 15900720, 16897590, 17283360, 18168150, 18209100, 18686910, 19340220, 20099940, 20359020, 20483340, 21028290, 21846360
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OFFSET
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1,1
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COMMENTS
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This sequence is a subsequence of A014574 (average of twin prime pairs), A249674 (divisible by 30) and A256753.
The numbers n - 37 and n + 1 belong to A156104 (p and p + 36 are primes) and A134117 (p where p + 36 is the next prime).
The numbers n - 37 and n - 1 belong to A271347 (p and p + 38 are primes).
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LINKS
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EXAMPLE
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1524180 is the average of the four consecutive primes 1524143, 1524179, 1524181, 1524217.
3264930 is the average of the four consecutive primes 3264893, 3264929, 3264931, 3264967.
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MATHEMATICA
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Select[Partition[Prime[Range[14*10^5]], 4, 1], Differences[#]=={36, 2, 36}&][[All, 2]]+1 (* Harvey P. Dale, Mar 12 2018 *)
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PROG
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(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 30000001, 6):
..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-37 and nextprime(i+1) == i+37 : print (i, end=', ')
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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