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%I #54 Sep 22 2021 08:09:29
%S 9,21,27,33,39,49,51,57,63,69,77,81,87,91,93,99,111,117,119,121,123,
%T 129,133,141,143,147,153,159,161,169,171,177,183,187,189,201,203,207,
%U 209,213,217,219,221,231,237,243,247,249,253,259,261,267,273,279,287
%N Composite numbers ending in 1, 3, 7 or 9.
%C Composite numbers not divisible by 2 or 5. - _Lekraj Beedassy_, Jul 05 2004
%C Composite numbers ending in 1, 3, 7 or 9 are values (some shared within sets, because some values are numbers with multiple factors) of the following sets of binomial products:
%C {(10x+3)*(10y+7), (10x+9)*(10y+9), (10x+11)*(10y+11)}, {(10x+3)*(10y+11), (10x+7)*(10y+9)},
%C {(10x+3)*(10y+9), (10x+7)*(10y+11)}, and
%C {(10x+3)*(10y+3), (10x+7)*(10y+7), (10x+9)*(10y+11)}, with x, y integers >= 0. - _Marvin Y. Hubble_, Jul 12 2013 and May 12 2014 and Sep 27 2019
%H Robert Israel, <a href="/A053795/b053795.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = 2.5n + 2.5n/log n + O(n/log^2 n). - _Charles R Greathouse IV_, Jan 30 2018
%p remove(isprime, [seq(seq(10*i+j,j=[3,7,9,11]),i=0..100)]); # _Robert Israel_, Jan 29 2018
%t Select[Range[300],CompositeQ[#]&&OddQ[#]&&!Divisible[#,5]&] (* _Harvey P. Dale_, Jul 13 2014 *)
%o (PARI) is(n)=gcd(n,10)==1 && !isprime(n) && n>1 \\ _Charles R Greathouse IV_, Jan 30 2018
%o (Python)
%o from sympy import isprime
%o def ok(n): return n > 1 and n%10 in {1, 3, 7, 9} and not isprime(n)
%o print(list(filter(ok, range(2, 288)))) # _Michael S. Branicky_, Sep 21 2021
%Y Subsequence of A045572.
%K nonn,base,easy
%O 1,1
%A _G. L. Honaker, Jr._, Apr 01 2000
%E More terms from _James A. Sellers_, Apr 08 2000
%E Offset corrected by _Arkadiusz Wesolowski_, Dec 18 2011
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