login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A215160 Odd numbers n with the property that the binary representation of n is the same as the decimal representation of the smallest multiple of n that can be represented with only 1's and 0's. 0
1, 21, 2231, 28261, 611123, 1200341, 3427673, 2202416417, 11102657671 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
All numbers that are a power of 2 times a member of the sequence share the property that the binary representation is the same as the decimal representation of the first 1's and 0's multiple.
Of the values listed, only 1200341 and 3427673 are primes. - Jonathan Vos Post, Aug 09 2012
LINKS
FORMULA
{odd n: n*A079339(n) = A007088(n)} . - R. J. Mathar, Aug 09 2012
EXAMPLE
For example 21*481=10101 (the first multiple of 21 containing only 1's and 0's) and the binary representation of 21 is 10101.
MAPLE
rebase := proc(n, bin, bout)
local a, c, i;
a := 0 ;
c := convert(n, base, bin) ;
add( op(i, c)*bout^(i-1), i=1..nops(c)) ;
end proc:
isA079339 := proc(n, c)
local c2, b;
if modp(c, n) > 0 then
return false;
end if;
c2 := rebase(c, 10, 2) ;
for b from 1 to c2-1 do
if modp( rebase(b, 2, 10), n) = 0 then
return false;
end if;
end do:
return true ;
end proc:
for n from 1 by 2 do
sb := rebase(n, 2, 10) ;
if isA079339(n, sb) then
print(n);
end if;
end do: # R. J. Mathar, Aug 09 2012
CROSSREFS
Cf. A079339.
Sequence in context: A119099 A319170 A359223 * A250062 A219000 A033510
KEYWORD
nonn,base,more
AUTHOR
Patrick McKinley, Aug 05 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 06:57 EDT 2024. Contains 371265 sequences. (Running on oeis4.)