login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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