[seqfan] Re: Observation on the divisors of 136
WALTER KEHOWSKI
wkehowski at cox.net
Sat Dec 30 19:28:21 CET 2017
Powers of two and 2^(2^n-1)*(2^(2^n)+1) for n=0,1,2,3,4 (the known Fermat primes). Interesting!
>
> On December 29, 2017 at 5:33 PM Jeremy Gardiner <jeremy.gardiner at btinternet.com> wrote:
>
> Consider the divisors of 136 (A018299):
>
> 1, 2, 4, 8, 17, 34, 68, 136.
>
> 136 in binary is 10001000.
>
> Reading off successive bits from the left we have:
>
> 1 1
> 10 2
> 100 4
> 1000 8
> 10001 17
> 100010 34
> 1000100 68
> 10001000 136
>
> This prompts the question, what other numbers have this property?
>
> i.e. Numbers whose successive binary shifted parts as decimal numbers are
> identical to their ordered divisors.
>
> Clearly, the powers of 2 have this property.
>
> Also for example 10 in binary is 1010 giving 1, 2, 5, 10.
>
> The sequence begins:
>
> 1, 2, 3, 4, 8, 10, 16, 32, ... but it is not A295296.
>
> Regards,
>
> Jeremy Gardiner
>
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