cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A153115 Positive integers with the same number of 1s in base 10 and base 2.

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%I A153115 #16 Jun 17 2020 10:23:14
%S A153115 1,16,128,512,1024,1152,2112,4112,8192,16384,16416,16512,131073,
%T A153115 131074,131076,131080,131081,131088,131105,131106,131108,131110,
%U A153115 131111,131113,131114,131116,131120,131121,131137,131138,131140,131141,131144,131152
%N A153115 Positive integers with the same number of 1s in base 10 and base 2.
%C A153115 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 A153115 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 A153115 Giovanni Resta, <a href="/A153115/b153115.txt">Table of n, a(n) for n = 1..10000</a> (first 250 terms from Robert Israel)
%e A153115 a(6)=1152 because 1152 base 2 = 10010000000 and both terms have the same number of ones.
%p A153115 filter:= proc(n) numboccur(1,convert(n,base,2))=numboccur(1,convert(n,base,10)) end proc:
%p A153115 select(filter, [$1..2*10^5]); # _Robert Israel_, Jun 16 2020
%Y A153115 Cf. A000120.
%K A153115 base,nonn,look
%O A153115 1,2
%A A153115 _Gil Broussard_, Dec 18 2008