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

1,3

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

Links

Table of n, a(n) for n=1..35.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A007088, A018826, A029943.

Sequence in context: A051505 A353720 A371294 * A335019 A337719 A289275

Adjacent sequences: A133405 A133406 A133407 * A133409 A133410 A133411

Keyword

base,nonn

Author

Jonathan Vos Post, Dec 22 2007

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

Status

approved