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.

A136318 Integers whose binary representation contains exactly two 1s, the 1s not being adjacent.

This page as a plain text file.
%I A136318 #17 Apr 07 2025 16:04:44
%S A136318 5,9,10,17,18,20,33,34,36,40,65,66,68,72,80,129,130,132,136,144,160,
%T A136318 257,258,260,264,272,288,320,513,514,516,520,528,544,576,640,1025,
%U A136318 1026,1028,1032,1040,1056,1088,1152,1280,2049,2050,2052,2056,2064,2080,2112,2176
%N A136318 Integers whose binary representation contains exactly two 1s, the 1s not being adjacent.
%C A136318 Subsequence of A018900. - _Chai Wah Wu_, Apr 07 2025
%H A136318 Chai Wah Wu, <a href="/A136318/b136318.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..99 from Gil Broussard)
%e A136318 a(1) = 5 = 101_2.
%e A136318 a(2) = 9 = 1001_2.
%e A136318 a(3) = 10 = 1010_2.
%e A136318 a(100) = 33024 = 1000000100000000_2.
%t A136318 Select[Range[2500],DigitCount[#,2,1]==2&&SequenceCount[IntegerDigits[#,2],{1,1}]==0&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 25 2017 *)
%o A136318 (Python)
%o A136318 from math import isqrt, comb
%o A136318 def A136318(n): return (1<<(m:=isqrt(n<<3)+1>>1)+1)+(1<<n-1-comb(m,2)) # _Chai Wah Wu_, Apr 07 2025
%Y A136318 Cf. A018900, A173589.
%K A136318 nonn,easy,base
%O A136318 1,1
%A A136318 _Gil Broussard_, Mar 24 2008