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A296012
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Primes of the form k + k+1 + k+2 +-1 where k, k+1, and k+2 are all composite numbers.
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2
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79, 101, 103, 149, 151, 167, 191, 193, 227, 229, 257, 277, 281, 283, 347, 349, 353, 359, 367, 373, 401, 431, 433, 439, 461, 463, 479, 509, 557, 563, 607, 613, 617, 619, 641, 643, 647, 653, 659, 661, 709, 733, 739, 743, 761, 797, 821, 823, 857, 859, 863, 887, 907, 911, 967, 971, 977, 983, 1019, 1021
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OFFSET
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1,1
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COMMENTS
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Primes p such that floor((p-2)/3) and floor((p-2)/3)+2 are composite. - Robert Israel, Dec 03 2017
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LINKS
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EXAMPLE
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25 + 26 + 27 + 1 = 79,
33 + 34 + 35 - 1 = 101,
33 + 34 + 35 + 1 = 103, etc.
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MAPLE
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filter:= proc(n) local k;
if not isprime(n) then return false fi;
k:= floor((n-2)/3);
not isprime(k) and not isprime(k+1) and not isprime(k+2)
end proc:
select(filter, [seq(i, i=5..2000, 2)]); # Robert Israel, Dec 03 2017
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MATHEMATICA
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Select[Join @@ Map[{{Total@ # - 1, #}, {Total@ # + 1, #}} &, Partition[Range@ 350, 3, 1]], And[PrimeQ@ First@ #, AllTrue[Last@ #, CompositeQ]] &][[All, 1]] (* Michael De Vlieger, Dec 03 2017 *)
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PROG
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(Python)
from __future__ import division
from sympy import nextprime, isprime
k = (p-2)//3
if not (isprime(k) or isprime(k+2)):
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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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