[seqfan] Re: Convert/concatenate/divide
M. F. Hasler
seqfan at hasler.fr
Wed Apr 25 13:44:44 CEST 2018
On Tue, Apr 24, 2018 at 3:18 PM, jnthn stdhr <jstdhr at gmail.com> wrote:
> For n > 0, covert n to its binary representation b, then let x equal the
> concatenation of the decimal values of each power of two <= n muliplied by
> its associated bit in b. If n divides x a(n) = n.
You mean, "add n to the list" (according to:
> (...) The sequence begins: 1, 2, 3, 4, 6, 8, 9, 10, 12, 16, 18,(...)
There are several variants:
- omit the 0's : concatenate only the values corresponding to nonzero bits
- instead of using the "decimal value of each power of two", use 1,2,3,...
(or rather ...3,2,1) (*)
- or another "canonical" sequence, e.g., the primes
- instead of concatenation, multiply or add (this would give back n
for "powers of two")
- consider the sequence(s) x(n), not only { n : n | x(n) }.
E.g., (*) would yield:
"concatenation of the indices of nonzero bits, starting with 1 for
the most/ least significant bit."
(could be concatenated in either direction)
Maybe not all of these (combinations) merit being added: these are
just some ideas...
- Maximilian
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