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A099019
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Odd composite numbers n such that n-2 and n+2 are also composite.
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3
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93, 117, 119, 121, 123, 143, 145, 185, 187, 203, 205, 207, 215, 217, 219, 245, 247, 287, 289, 297, 299, 301, 303, 321, 323, 325, 327, 341, 343, 363, 393, 405, 413, 415, 425, 427, 453, 471, 473, 475, 483, 495, 513, 515, 517, 527, 529, 531, 533, 535, 537, 551
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OFFSET
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1,1
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COMMENTS
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Goldbach's conjecture states that all even numbers > 2 can be expressed as the sum of two primes. If true, then this sequence contains all composites which cannot be expressed as the sum or difference of two primes. - Bob Selcoe, Mar 10 2015
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LINKS
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EXAMPLE
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93 is the first term because 91=7*13, 93=3*31 and 95=5*19 are all composite and there is no smaller odd composite with both odd neighbors composite.
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MATHEMATICA
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Select[Range@1200, OddQ@# && AllTrue[{# - 2, #, # + 2}, CompositeQ] &] (* Michael De Vlieger, Mar 10 2015, Version 10 *)
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PROG
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(PARI) forstep(n=9, 1000, 2, if(!isprime(n)&&!isprime(n-2)&&!isprime(n+2), print1(n, ", ")))
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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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