A065880 Largest positive number that is n times the number of 1's in its binary expansion, or 0 if no such number exists.

0, 1, 2, 6, 4, 10, 12, 21, 8, 18, 20, 55, 24, 0, 42, 60, 16, 34, 36, 0, 40, 126, 110, 115, 48, 0, 0, 108, 84, 116, 120, 155, 32, 66, 68, 0, 72, 222, 0, 156, 80, 246, 252, 172, 220, 180, 230, 0, 96, 0, 0, 204, 0, 318, 216, 0, 168, 285, 232, 295, 240, 366, 310, 378, 64, 130

Offset: 0

Author

Henry Bottomley, Nov 26 2001

Keywords

• base
• nonn

Comments

a(n) is bounded above by n*A272756(n), so a program only has to check values up to that point to see if a(n) is zero. - Peter Kagey, May 05 2016

Examples

			a(23)=115 since 115 is written in binary as 1110011 and 115/(1+1+1+0+0+1+1)=23 and there is no higher possibility (if k is more than 127 then k divided by its number of binary 1's is more than 26).
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000

Crossrefs

A052489 is the base 10 equivalent.

Cf. A000120, A049445, A058898, A065413, A065878, A065879, A272756.

Programs

Mathematica

Table[SelectFirst[Reverse@ Range@ #, First@ DigitCount[#, 2] == #/n &] &[n SelectFirst[Range[2^12], # > IntegerLength[n #, 2] &]], {n, 80}] /. k_ /; MissingQ@ k -> 0 (* Michael De Vlieger, May 05 2016, Version 10.2 *)