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A309005
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Odd squarefree composite numbers m such that m+2 is prime.
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1
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15, 21, 35, 39, 51, 57, 65, 69, 77, 87, 95, 105, 111, 129, 155, 161, 165, 177, 195, 209, 221, 231, 237, 249, 255, 267, 291, 305, 309, 329, 335, 345, 357, 365, 371, 377, 381, 395, 399, 407, 417, 429, 437, 447, 455, 465, 485, 489, 497, 501, 519, 545, 555, 561, 591, 597, 611
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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15 = 3*5 is the smallest squarefree composite number m such that m+2 is prime; 15+2=17.
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MAPLE
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with(NumberTheory):
N := 500;
for n from 2 to N do
if IsSquareFree(n) and not mod(n, 2) = 0 and not isprime(n) and isprime(n+2) then print(n);
end if:
end do:
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MATHEMATICA
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Select[Range[15, 611, 2], And[CompositeQ@ #, SquareFreeQ@ #, PrimeQ[# + 2]] &] (* Michael De Vlieger, Jul 08 2019 *)
Select[Prime[Range[2, 150]]-2, SquareFreeQ[#]&&CompositeQ[#]&] (* Harvey P. Dale, Dec 03 2022 *)
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PROG
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(PARI) isok(n) = isprime(n+2) && (n%2) && (n>1) && !isprime(n) && issquarefree(n); \\ Michel Marcus, Jul 05 2019
(Magma) [n: n in [2..611] | IsPrime(n+2) and not IsPrime(n) and IsSquarefree(n)]; // Vincenzo Librandi, Jul 07 2019
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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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