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Numbers of the form 2^i*3^j*(12k+7) or 2^i*3^j*(12k+11), i, j, k >= 0.
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%I #24 Nov 14 2023 04:36:51

%S 7,11,14,19,21,22,23,28,31,33,35,38,42,43,44,46,47,55,56,57,59,62,63,

%T 66,67,69,70,71,76,79,83,84,86,88,91,92,93,94,95,99,103,105,107,110,

%U 112,114,115,118,119,124,126,127,129,131,132,134,138,139,140

%N Numbers of the form 2^i*3^j*(12k+7) or 2^i*3^j*(12k+11), i, j, k >= 0.

%C The asymptotic density of this sequence is 1/2. - _Amiram Eldar_, Nov 14 2023

%H Amiram Eldar, <a href="/A225858/b225858.txt">Table of n, a(n) for n = 1..10000</a>

%e From _David A. Corneth_, Nov 11 2023: (Start)

%e 28 = 2^2 * 7 = 2^2 * 3^0 * (12*0 + 7) is in the sequence as it meets the first form.

%e 76 = 2^2 * 19 = 2^2 * 3^0 * (12*1 + 7) is in the sequence as it meets the first form.

%e 15 = 3 * 5 = 2^0 * 3^1 * (12*0 + 5) is not in the sequence as it does not match any of the desired forms. (End)

%t Select[Range[140], Mod[#/Times @@ ({2, 3}^IntegerExponent[#, {2, 3}]), 4] == 3 &] (* _Amiram Eldar_, Nov 14 2023 *)

%o (PARI) for(n=1,200,t=n/(2^valuation(n,2)*3^valuation(n,3));if((t%4==3),print1(n,",")))

%o (Magma) [n: n in [1..200] | d mod 4 eq 3 where d is n div (2^Valuation(n,2)*3^Valuation(n,3))]; // _Bruno Berselli_, May 16 2013

%Y Complement of A225857. Cf. A225838.

%K nonn,easy

%O 1,1

%A _Ralf Stephan_, May 18 2013

%E Name clarified by _Peter Munn_, Nov 11 2023