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

407, 493, 893, 1189, 1343, 1403, 1643, 1681, 1961, 3151, 3223, 4063, 4579, 7087, 7597, 7979, 8791, 9167, 10579, 11227, 13303, 14219, 15487, 16147, 23479, 24341, 25751, 26101, 27571, 28757, 30461, 30607, 33431, 34093, 35417, 36349, 39917

Offset: 1

Author

Robert G. Wilson v, Aug 08 2001; corrected Nov 13 2002

Keywords

• base
• nonn

Examples

			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).
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A002808, A062238.

Programs

Mathematica

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