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%I #40 Jul 27 2023 22:32:26
%S 25,33,49,55,63,75,85,91,93,115,117,119,121,123,133,141,143,145,153,
%T 159,169,175,183,185,187,201,203,205,207,213,215,217,219,235,243,245,
%U 247,253,259,265,273,285,287,289,295,297,299,301,303,319,321,323,325,327,333
%N Smaller of two consecutive odd numbers that are composites.
%C Analogous to A001359 for odd composite numbers (A071904).
%C Consists of numbers that cannot be the difference of two primes: an odd number m can be the difference of two primes only if m+2 is prime, which cannot be the case for any a(n) as a(n)+2 is composite.
%C Some terms form subsequences of perfect powers, e.g., A106564 (for squares) and A269346 (for cubes).
%C Any composite of the form 6k+1 (A016921) is a term: (6k+1)+2 = 3(2k+1) is both odd and composite as a product of two odd numbers, thus 6k+1, being odd, is a term if it is composite.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TwinComposites.html">Twin Composites</a>
%F a(n) = A061673(n) - 1. - _M. F. Hasler_, Nov 18 2018
%e 25 belongs to this sequence because 27=25+2 is the next odd composite.
%t Select[Range[450], OddQ[#]&& !PrimeQ[#]&&!PrimeQ[#+2]&]
%o (PARI) for(n=1, 450, n%2==1&&!isprime(n)&&!isprime(n+2)&&print1(n, ", "))
%o (Magma) [n: n in [1..350]| not IsPrime(n) and not IsPrime(n+2) and n mod 2 eq 1]; // _Vincenzo Librandi_, Feb 28 2016
%Y Cf. A071904 (odd composites), A001359 (similar sequence for primes).
%Y Cf. A106564, A269346.
%Y Cf. A061673.
%K nonn
%O 1,1
%A _Waldemar Puszkarz_, Feb 24 2016
%E Name edited by _Michel Marcus_, Jul 27 2023
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