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%I #19 Sep 22 2020 00:38:41
%S 4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,
%T 52,54,55,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,91,92,
%U 94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128
%N Composite numbers which in base 2 contain their largest proper factor as a substring.
%C This is also the set of highest rolls that can be made with some number of platonic dice (dice which are platonic solids, considered to be the most "fair" dice). For instance, 22 is the highest roll with a die which is a dodecahedron, a cubic die, and a tetrahedral die. - _Joshua R. Tint_, Sep 08 2020
%C Contains every even number > 2. Odd terms are A063131. - _David A. Corneth_, Sep 09 2020
%e 55 is in the sequence as 55 = 110111_2 and the largest proper divisor of 55 is 11 and 11 = 1011_2 which is contained in 110111_2. - _David A. Corneth_, Sep 08 2020
%t Do[ If[ !PrimeQ[ n ] && StringPosition[ ToString[ FromDigits[ IntegerDigits[ n, 2 ] ] ], ToString[ FromDigits[ IntegerDigits[ Divisors[ n ] [ [ -2 ] ], 2 ] ] ] ] != {}, Print[ n ] ], {n, 2, 150} ]
%Y Cf. A062238, A063131.
%K nonn,easy,base
%O 1,1
%A _Robert G. Wilson v_, Aug 08 2001