[seqfan] Re: Correction to A093848 Variation on Golomb's sequence(anti-Golomb)(2)

[Eric Angelini]

The next step being that S embeds the instructions for Scomp
and Scomp embeds the instructions for S. I'm working on that...
Best,
É.


-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu] De la part de Eric Angelini
Envoyé : mardi 22 juin 2010 15:38
À : Sequence Fanatics Discussion list
Objet : [seqfan] Re: Correction to A093848 Variation on Golomb's sequence(anti-Golomb)


Hello Jeremy,
your PS gives me the idea of a (nice?) seq. -- a kind of "anti-Golomb"
variation:

S=1,3,4,6,8,10,12,13,15,17,19,21,23,25,26,28,30,32,34,36,38,40,42,43,
  45,47,49,51,53,55,57,59,61,63,64,66,68,70,72,74,76,78,80,82,84,86,88,
  90,91,93,...

... where the complementary of S gives the size of the parity runs:

Scomp=2,5,7,9,11,14,16,18,20,22,24,27,29,31,33,35,37,39,41,44,46,...

S was build with the rule [1] that you cannot insert any integer between
two "touching" runs (run 1,3 is followed by 4,6,8,10,12; there is no
integer between 3 and 4) and [2] that S and Scomp share no integer.

I like the idea that the complementary of S embeds the "instructions"
for S. This could be used elsewhere -- and might have been already
(there is such a flavour in the famous Hofstadter seq. where the
first differences of H never appear in H).

Best,
É.


-----Message d'origine-----
De : seqfan-bounces at list.seqfan.eu [mailto:seqfan-bounces at list.seqfan.eu] De la part de Jeremy Gardiner
Envoyé : mardi 22 juin 2010 11:27
À : Sequence Fanatics Discussion list
Objet : [seqfan] Correction to A093848 Variation on Golomb's sequence


A093848 Variation on Golomb's sequence - earliest monotonic sequence
starting with a(1)=1 and satisfying a(n)=length of n-th run of consecutive
integers with same parity:

1,2,4,5,7,9,11,12,14,16,18,20,21,23,25,27,29,31,33,34,36,38,40,42,44,46,48,5
0,51,53,55,57,59,61,63,65,67,69,71,72,74,76,78,80,82,84,86,88,90,92,94,96,98
,99,101,103,105,107,109,111,113,115,117,119,121,

I get (by hand):
1,2,4,5,7,9,11,12,14,16,18,20,21,23,25,27,29,31,33,34,36,38,40,42,44,46,48,5
0,51,53,55,57,59,61,63,65,67,69,71,72,74,76,78,80,82,84,86,88,90,92,94,95,97
,99,101,103,105,107,109,111,113,115,117,119,121,

It's slightly worrying that I've noticed errors in three sequences in the
OEIS in the last week - in the other cases these were missing terms,
possibly due to transcription errors when submitting:

I would urge submitters to check that all the terms in their sequences
appear correctly in the OEIS!

Jeremy Gardiner

PS
Perhaps the complementary sequence may interesting? (not in the OEIS):

3,6,8,10,13,15,17,19,22,24,26,28,30,32,35,37,39,41,43,45,47,49,52,54,56,58,6
0,62,64,66,68,70,73,75,77,79,81,83,85,87,89,91,93,96,98,100,102,104,106,108,
110,112,114,116,118,120,123




_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/



_______________________________________________

Seqfan Mailing list - http://list.seqfan.eu/