[seqfan] A034881 comment and variation

Rainer Rosenthal r.rosenthal at web.de
Fri Nov 30 17:44:59 CET 2012


Sequence a = A034881 has elements a(0) upto a(14).


*comment*

Isn't a(14) = 1.8216437241240*10^13?
If so, then this comment in EXTENSIONS makes no sense any more:

  " a(14) > 1.04*10^13 (if it exists)"

The last comment should  be changed to

" a(15) > 2*10^16, Don Reble (djr)(AT)nk.ca), Oct 15 2012"

Do you agree?


*variations*

The definition of A034881 reads
"Smallest number a(n) such that a(n)a(n-i)-1 is prime for all i."

But if you allow a(0)=0 then there is no a(1) any more.
The sequence then becomes finite, consisting of a(0)=0 alone.

So it should better be stated
"Smallest number a(n) > 0 such that a(n)a(n-i)-1 is prime for all i."

Even now there are two possibilities. The sequence A034881 evolves only
if this is read as:
"Smallest number a(n) > 0 such that a(n)a(n-i)-1 is prime for all i > 0."

Otherwise, allowing i=0, we require a(n)a(n) to be prime, too. The
sequence which emerges from the definition
"Smallest number a(n) > 0 such that a(n)a(n-i)-1 is prime for all i >= 0."
starts as follows:
1, 2, 6, 156, 4260, 117306, 160650

(I checked this only upto 600000. Sequence is not in the OEIS.)

Cheers,
Rainer Rosenthal
r.rosenthal at web.de








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