A133408 Numbers k such that k is a substring of both its square and its cube in base 2 (written in base 10).

0, 1, 2, 4, 8, 16, 32, 41, 64, 128, 256, 512, 1024, 2048, 4096, 8192, 16384, 32768, 65536, 131072, 262144, 524288, 1048576, 2097152, 4194304, 8388608, 16777216, 33554432, 67108864, 134217728, 268435456, 536870912, 1073741824, 2147483648, 4294967296

Offset: 1

Author

Jonathan Vos Post, Dec 22 2007

Keywords

• base
• nonn

Comments

Binary analog of A029943. Subset of A018826.

Row 2 of array whose row 1 is A002275 and whose row 10 is A029943.

Contains every power of 2. Is 41 the only term which is not a power of 2? - Sean A. Irvine, Oct 11 2009

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

Examples

			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.
		

Crossrefs

Cf. A007088, A018826, A029943.

Programs

Mathematica

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 *)

Formula

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

Extensions

Corrected and extended by Sean A. Irvine, Oct 11 2009

a(32) from Oliver Allen, Aug 08 2017

a(33)-a(35) from Oliver Allen, Aug 10 2017