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.
%I A133408 #32 Mar 19 2025 23:33:46
%S A133408 0,1,2,4,8,16,32,41,64,128,256,512,1024,2048,4096,8192,16384,32768,
%T A133408 65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,
%U A133408 33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296
%N A133408 Numbers k such that k is a substring of both its square and its cube in base 2 (written in base 10).
%C A133408 Binary analog of A029943. Subset of A018826.
%C A133408 Row 2 of array whose row 1 is A002275 and whose row 10 is A029943.
%C A133408 Contains every power of 2. Is 41 the only term which is not a power of 2? - _Sean A. Irvine_, Oct 11 2009
%C A133408 Up to 1.7*10^13 the sequence does not contain numbers greater than 41 which are not a power of 2. - _Giovanni Resta_, Aug 30 2018
%F A133408 {k such that A007088(k) is a substring of A007088(k^2) and is a substring of A007088(k^3)}.
%e A133408 41 is a term because 41 (base 2) = 101001, which is a substring of 41^2 (base 2) = 11010010001 and which is a substring of 41^3 (base 2) = 10000110100111001.
%t A133408 Select[Range[0,10^6],SequenceCount[IntegerDigits[#^2,2],IntegerDigits[#,2]]>0&&SequenceCount[IntegerDigits[#^3,2],IntegerDigits[#,2]]>0&] (* _James C. McMahon_, Mar 17 2025 *)
%Y A133408 Cf. A007088, A018826, A029943.
%K A133408 base,nonn
%O A133408 1,3
%A A133408 _Jonathan Vos Post_, Dec 22 2007
%E A133408 Corrected and extended by _Sean A. Irvine_, Oct 11 2009
%E A133408 a(32) from _Oliver Allen_, Aug 08 2017
%E A133408 a(33)-a(35) from _Oliver Allen_, Aug 10 2017