|
%I #16 Jun 17 2020 10:23:14
%S 1,16,128,512,1024,1152,2112,4112,8192,16384,16416,16512,131073,
%T 131074,131076,131080,131081,131088,131105,131106,131108,131110,
%U 131111,131113,131114,131116,131120,131121,131137,131138,131140,131141,131144,131152
%N Positive integers with the same number of 1s in base 10 and base 2.
%C Some have exactly one 1. These are exclusively of the form 2^n, but not universally. 512 = 1000000000b, 1 one. 2048 = 100000000000b but 2048 lacks a 1 digit. The smallest integer with 6 ones in both decimal and binary bases is 11011112 = 101010000000010000101000b.
%C If n is in the sequence and n == 0, 5, 9, 10, 13 or 17 (mod 20) or 11 (mod 40), then n+1 is in the sequence. - _Robert Israel_, Jun 17 2020
%H Giovanni Resta, <a href="/A153115/b153115.txt">Table of n, a(n) for n = 1..10000</a> (first 250 terms from Robert Israel)
%e a(6)=1152 because 1152 base 2 = 10010000000 and both terms have the same number of ones.
%p filter:= proc(n) numboccur(1,convert(n,base,2))=numboccur(1,convert(n,base,10)) end proc:
%p select(filter, [$1..2*10^5]); # _Robert Israel_, Jun 16 2020
%Y Cf. A000120.
%K base,nonn,look
%O 1,2
%A _Gil Broussard_, Dec 18 2008
|
