[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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