A133408 - OEIS

%I #25 Aug 30 2018 08:20:06

%S 0,1,2,4,8,16,32,41,64,128,256,512,1024,2048,4096,8192,16384,32768,

%T 65536,131072,262144,524288,1048576,2097152,4194304,8388608,16777216,

%U 33554432,67108864,134217728,268435456,536870912,1073741824,2147483648,4294967296

%N Numbers n such that n is a substring of both its square and its cube in base 2 (written in base 10).

%C Binary analog of A029943. Subset of A018826. Row 2 of array whose row 1 is A002275 and whose row 10 is A029943.

%C Contains every power of 2. Is 41 the only term which is not a power of 2? - _Sean A. Irvine_, Oct 11 2009

%C 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 {k such that A007088(k) is a substring of A007088(k^2) and is a substring of A007088(k^3)}.

%e a(7) = 41 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.

%Y Cf. A007088, A018826, A029943.

%K base,nonn

%O 1,3

%A _Jonathan Vos Post_, Dec 22 2007

%E Corrected and extended by _Sean A. Irvine_, Oct 11 2009

%E a(32) from _Oliver Allen_, Aug 08 2017

%E a(33)-a(35) from _Oliver Allen_, Aug 10 2017