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

0,3

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

Links

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

Example

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).

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 *)

Crossrefs

A052489 is the base 10 equivalent.

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

Sequence in context: A245579 A245788 A065879 * A335063 A371285 A090546

Adjacent sequences: A065877 A065878 A065879 * A065881 A065882 A065883

Keyword

base,nonn

Author

Henry Bottomley, Nov 26 2001

Status

approved