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A133408
Numbers n such that n is a substring of both its square and its cube in base 2 (written in base 10).
0
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
FORMULA
{k such that A007088(k) is a substring of A007088(k^2) and is a substring of A007088(k^3)}.
EXAMPLE
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.
CROSSREFS
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