[seqfan] The discriminator of a sequence (continued)

Neil Sloane njasloane at gmail.com
Tue May 10 17:01:54 CEST 2016


Olivier, Maximilian, Marc, you said several things, and this is a followup:

1. Me: Given that the search mechanism doesn't work (discriminator"
gets mapped to "discriminant", and there is no way to tell the search that
the former
is the word you really want), I created an entry in the OEIS Index.

Ideally there would be a link from each of the sequences to
this index page but I did not have time to do that

2. Olivier said:

(start)
A062383 <http://oeis.org/A062383 1, 2, 4, 4, 8, 8, 8, 8, 16, 16, 16, 16,
16, 16, 16, 16, 32, 32, 32,... but we need to make a comment about it. DONE

The Discriminator of evil numbers starts 1, 2, 4, 4, 7, 8, 8, 8, 13, 16,
16, 16, 16, 16, 16, 16, 31, 32, but is not in the OEIS. IT IS NOW

Another related transform is the compressed or reduced version of the
Discriminator
and its change index for sequences who stay with the same modulo for quite
some time.

The compressed Discriminator of odious numbers as well as (n choose 2)
is just the powers of 2 and the one for factorial is

1, 2, 3, 7, 10, 13, 31, 37, 61, 83, 127, 179, 193, 277, 383, 479, 541, 641,
877, ... (not in the OEIS) I CREATED A272649 FOR THIS BUT IT NEEDS WORK
(needs definition, program, etc)

and for 2^n -1  or  2^n+1  is 1, 3, 5, 9, 11, 13, 19, 25, 29, 37, 53, 59,
61, 67, 83, 101, and seems to be A139099 <http://oeis.org/A139099> CAN YOU
PLEASE ADD A COMMENT

for 3^n-1 or 3^n+1 1, 4, 5, 7, 17, 19, 25, 29, 31, 43, 53, 79, 89,
101, ... (not
in the OEIS) SAME THING

The Discriminator for integer partitions with distinct parts is

1, 3, 4, 4, 5, 6, 7, 8, 10, 12, 14, 17, 20, 24, 29, 34, 40, 48, 56,
66, 78, 91, 106, 124, 144, 167, 194, 224, 258, 298, ...

(not in the OEIS) PLEASE ADD IT

and the compressed one for integer partitions is

1, 2, 3, 5, 7, 11, 16, 42, 52, 68, 80, 83, 84, 101, 116

(not in the OEIS) SAME THING

When you add these, please also update the Index entry!
(end)

3. Maximilian also responded, but I don't know if he suggested any new
sequences.

4.  Marc suggested other examples in a private email to me - Marc, would
you please add them? I refer to these (and others):

I think the sequence of least discriminators begins (pace quibbles re. 0)
  0 1 1 2 1 3 2 3 1 2 3 4 ... Not in OEIS?

And (barring misteaks) the sequence of greatest confusers (ditto, arguably)
  0 0 0 1 0 2 1 1 0 3 2 3 ... Not in OEIS?

Neil


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