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 A099019 Odd composite numbers n such that n-2 and n+2 are also composite. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS No term is the difference of two primes. - Juri-Stepan Gerasimov, Oct 10 2009 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 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 Wikipedia, Goldbach's conjecture EXAMPLE 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. MATHEMATICA Select[Range@1200, OddQ@# && AllTrue[{# - 2, #, # + 2}, CompositeQ] &] (* Michael De Vlieger, Mar 10 2015, Version 10 *) PROG (PARI) forstep(n=9, 1000, 2, if(!isprime(n)&&!isprime(n-2)&&!isprime(n+2), print1(n, ", "))) CROSSREFS Subsequence of A007921. Sequence in context: A020320 A039550 A167776 * A082131 A249300 A153684 Adjacent sequences: A099016 A099017 A099018 * A099020 A099021 A099022 KEYWORD nonn AUTHOR Rick L. Shepherd, Nov 13 2004 STATUS approved

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Last modified August 14 15:29 EDT 2024. Contains 375165 sequences. (Running on oeis4.)