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A065880 Largest positive number that is n times the number of 1's in its binary expansion, or 0 if no such number exists. 8

%I

%S 0,1,2,6,4,10,12,21,8,18,20,55,24,0,42,60,16,34,36,0,40,126,110,115,

%T 48,0,0,108,84,116,120,155,32,66,68,0,72,222,0,156,80,246,252,172,220,

%U 180,230,0,96,0,0,204,0,318,216,0,168,285,232,295,240,366,310,378,64,130

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

%C 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

%H Peter Kagey, <a href="/A065880/b065880.txt">Table of n, a(n) for n = 0..10000</a>

%e 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).

%t 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 *)

%Y A052489 is the base 10 equivalent.

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

%K base,nonn

%O 0,3

%A _Henry Bottomley_, Nov 26 2001

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Last modified November 19 22:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)