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 A063138 Composite numbers not divisible by 2, 3, 5 or 7 which in base 2 contain their largest proper factor as a substring. 2

%I

%S 407,493,893,1189,1343,1403,1643,1681,1961,3151,3223,4063,4579,7087,

%T 7597,7979,8791,9167,10579,11227,13303,14219,15487,16147,23479,24341,

%U 25751,26101,27571,28757,30461,30607,33431,34093,35417,36349,39917

%N Composite numbers not divisible by 2, 3, 5 or 7 which in base 2 contain their largest proper factor as a substring.

%H Amiram Eldar, <a href="/A063138/b063138.txt">Table of n, a(n) for n = 1..10000</a>

%e 407 is in the sequence because 407_d = 110010111_b and its largest proper divisor is 37_d = 100101_b is a substring. Also 407 is not prime nor congruent to 0 (modulo either 2, 3, 5 or 7).

%t a = {}; Do[ If[ !PrimeQ[n] && Sort[Mod[n, {3, 5, 7}]][[1]] != 0 && StringPosition[ ToString[ FromDigits[ IntegerDigits[n, 2]]], ToString[ FromDigits[ IntegerDigits[ Divisors[n][[ -2]], 2]]]] != {}, a = Append[a, n]], {n, 3, 39960, 2}]; a

%Y Cf. A002808, A062238.

%K base,nonn

%O 1,1

%A _Robert G. Wilson v_, Aug 08 2001; corrected Nov 13 2002

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Last modified December 9 07:21 EST 2021. Contains 349627 sequences. (Running on oeis4.)