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A271323
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Numbers n such that n - 41, n - 1, n + 1, n + 41 are consecutive primes.
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1
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383220, 1269642, 1528938, 2590770, 3014700, 3158298, 3697362, 3946338, 4017312, 4045050, 4545642, 4711740, 4851618, 4871568, 5141178, 5194602, 5925042, 5972958, 5990820, 6075030, 6179862, 6212202, 6350760, 6442938, 6549312, 6910638, 6912132
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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) 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 - 40 and n + 1 belong to A126721 (p such that p + 40 is the next prime) and A271981 (p and p + 40 are primes).
The numbers n - 40 and n - 1 belong to A271982 (p and p + 42 are primes).
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LINKS
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EXAMPLE
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383220 is the average of the four consecutive primes 383179, 383219, 383221, 383261.
1269642 is the average of the four consecutive primes 1269601, 1269641, 1269643, 1269683.
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MATHEMATICA
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Mean/@Select[Partition[Prime[Range[472000]], 4, 1], Differences[#] == {40, 2, 40}&] (* Harvey P. Dale, Oct 16 2021 *)
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PROG
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(Python)
from sympy import isprime, prevprime, nextprime
for i in range(0, 12000001, 6):
..if isprime(i-1) and isprime(i+1) and prevprime(i-1) == i-41 and nextprime(i+1) == i+41: 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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