comments and derived seqs re: A124168

Jonathan Post jvospost3 at gmail.com
Mon Dec 4 22:15:44 CET 2006


I don't want to bombard Dr. Neil J. A. Sloane with sequences that I make up,
so as to not interrupt his holiday-ish December.

However, I have some reactions to:

A124168 Union of all n-Fibonacci sequences (starting with 0, ..., 0, 1).

The author should refer to MathWorld's entry on n-step Fibonacci, for the
proper terminology, and the reference by the wonderful Tony Noe on all
primes in that union. I have also, I vaguely recall, dealt the sequence of
semiprimes in that union, but don't recall if I'd submitted it to OEIS.

I would suggest attention to the complement sequence, numbers which do not
occur in any n-step Fibonacci number (starting with (0, 0, 0, ..., 1).

 9, 10, 11, 12, 14, 17, 18, 19, 20, 22, 23, 25, 26, 27, 28, 30, 33, 35, 36,
37, 38, 39, 40, 41, 42, 43, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 58,
59, 60, 62, 65, ...

and the the analogue of the union of all n-step Lucas numbers, and the
complement of that.

-- Jonathan
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