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.

1, 21, 2231, 28261, 611123, 1200341, 3427673, 2202416417, 11102657671

Offset: 1

Author

Patrick McKinley, Aug 05 2012

Keywords

• nonn
• base
• more

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

Examples

			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.
		

Crossrefs

Cf. A079339.

Programs

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

Formula

{odd n: n*A079339(n) = A007088(n)} . - R. J. Mathar, Aug 09 2012