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A271349
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Numbers n such that n - 35, n - 1, n + 1 and n + 35 are consecutive primes.
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1
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276672, 558828, 1050852, 1278288, 1486908, 1625418, 2536308, 2538918, 2690958, 2731242, 3015162, 3252678, 3268338, 3508278, 3711612, 4233708, 4575912, 4717962, 5004402, 5108352, 5404032, 5482782, 5519082, 5525328, 5640918, 5654358, 5995818
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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 2 (resp. 8) are congruent to 12 (resp. 18) mod 30.
The numbers n - 35 and n + 1 belong to A252091 (p and p + 34 are primes) and A134116 (p such that p + 34 is the next prime).
The numbers n - 35 and n - 1 belong to A156104 (p and p + 36 are primes).
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LINKS
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EXAMPLE
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276672 is the average of the four consecutive primes 276637, 276671, 276673, 276707.
558828 is the average of the four consecutive primes 558793, 558827, 558829, 558863.
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MATHEMATICA
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Select[Partition[Prime[Range[500000]], 4, 1], Differences[#]=={34, 2, 34}&] [[All, 2]]+1 (* Harvey P. Dale, Oct 11 2017 *)
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PROG
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(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-35 and nextprime(i+1) == i+35 : 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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