[seqfan] Re: First "stringed" sequence as a whole

[Lars Blomberg]

Hello,

After a fair amount of hacking, I suggest the following sequence
F = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 90, 92, 93, 12, 22, 91, 18, 11, 13, 
14, 15, 21, 19, 16, 17, 20, 29, 23, 30, 39, 24, 25, 26, 32, 27, 28, 31, 37, 
94, 95, 34, 48, 33, 35, 81, 49, 59, 40, 36, 38, 58, 41, 96, 69, 50, 43, 79, 
42, 44, 82, 45, 51, 46, 80, 47, 52, 84, 53, 54, 55, 56, 61, 85, 97, 57, 60, 
62, 64, 83, 63, 65, 66, 67, 98, 99, 68, 909, 86, 87, 70, 88, 71, 72, 89, 73, 
75, 299, 74, 900, 801, 800, 77, 78, 100, 76, 101, 191, 802, 200, 110, 111, 
112, 220, 119, 113, 120, 114, 180, 115, 116, ... to 1400 terms.

The corresponding indices of the digits visited starts like this
0, 1, 3, 7, 15, 18, 20, 23, 25, 16, 6, 13, 14, 4, 9, 19, 22, 12, 2, 5, 11, 
10, 8, 17, 21, 24, 26, 28, 30, 32, 34, 31, 36, 38, 40, 42, 45, 35, 37, 27, 
29, 33, 39, 46, 43, 44, 47, 51, 41, 49, 50, 54, 57, 64, 68, ... to 4500 
terms.
These values follow the diagonal y=x quite nicely on the average, but of 
course fluctuates around it.

Of the total times that F changes length during the search, 90% are 
increments and 10% are decrements=backtracking.
Backtracking is never needed more that once at a time.
While this is reassuring, we can not be sure (at least I cannot) that a long 
way up there arises the need for a massive backtrack,
maybe even down to the very first terms.

The above F being a guess, should it still be entered into the OEIS?

/Lars B


-----Ursprungligt meddelande----- 
From: Eric Angelini
Sent: Tuesday, July 15, 2014 3:16 PM
To: Sequence Fanatics Discussion list
Subject: [seqfan] First "stringed" sequence as a whole





Hello Seqfans,

The « stringed numbers » (here: https://oeis.org/A244890 )

are a good start to appreciate (?) what is going on below.



a) we want a seq F with no repeated term

b) F being the lexicographically first

c) with the "stringed" property seen as a whole.



F = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 90, 98, 12, 11, 14, 13, 15, 16, 17, 
18, 29, 19, 20, 39, 2a, 49, bc, ...

(digits a, b and c (at the end) are not yet known by the author).



We want to visit once and only once every digit of F, starting

with both "feet" on the first digit (0), and simply obeying to

the "stringed" rule: when you land on a digit "d", jump over

d digits, to the left or to the right, and proceed from there

(landing on a zero forces you to proceed with the digit

immediately on your left or on your right).



Notation for this e-mail:



A digit followed by a plus sign means "now jump to the right" ;

a digit preceded by a minus sign means "now jump to the left".



We have here the jumps' succession (showed on separate lines,

each line having jumps in the same direction):



Fb=0+,1+,2,3+,4,5,6,7+,8,9,10,90,9-8,12,11,14,13,15,16,17,18,29,19,20,39,2a,49,bc,

Fc=0,1,2,3,4,5,6+,7,8,9,10,90,9-8,12,11,14,13,15,16,17,18,29,19,20,39,2a,49,bc,

Fd=0,1,2,3,4,5,6+,7,8,9,10,9-0,98,12,11,14,13,15,16,17,18,29,19,20,39,2a,49,bc,

Fe=0,1,2+,3,4,5,6,7,8,9,10,-90,98,12,11,14,13,15,16,17,18,29,19,20,39,2a,49,bc,

Ff=0,1,2+,3,4,5,6,7,8,9,1-0,90,98,12,11,14,13,15,16,17,18,29,19,20,39,2a,49,bc,

Fg=0,1,2,3,4,5,6,7,8+,9,-10,90,98,12,11,14,13,15,16,17,18,29,19,20,39,2a,49,bc,

Fh=0,1,2,3,4,5,6,7,8+,9,10,90,98,1-2,11,14,13,15,16,17,18,29,19,20,39,2a,49,bc,

Fi=0,1,2,3,4+,5,6,7,8,9,10,90,-98,1-2,11,14,13,15,16,17,18,29,19,20,39,2a,49,bc,

Fj=0,1,2,3,4+,5,6,7,8,9+,10,90,98,12,11+,1-4,13,15,16,17,18,29,19,20,39,2a,49,bc,

Fk=0,1,2,3,4,5,6,7,8,9,10,90,98,1+2,11,1-4,13,15,16,17,18,29,19,20,39,2a,49,bc,

Fl=0,1,2,3,4,5,6,7,8,9,10,90,98,1+2,1+1,1+4,1+3,1+5,1+6,1+7,1+8,2+9,1-9,20,39,2a,49,bc,

Fm=0,1,2,3,4,5,6,7,8,9,10,90,98,12,11,14,13,15+,16,17,18,29,1-9,20,39,2a,49,bc,

Fn=0,1,2,3,4,5,6,7,8,9,10,90,98,12,11,14,13,15+,16,17,18+,29,19,20,39,2+a,4-9,bc,

Fo=0,1,2,3,4,5,6,7,8,9,10,90,98,12,11,14,13+,15,16,17,18,2-9,19,20,39,2a,4-9,bc,

Fp=0,1,2,3,4,5,6,7,8,9,10,90,98,12,11,14,13+,15,16+,17,18,29,1+9,2+0,3-9,2a,49,bc,

Fq=0,1,2,3,4,5,6,7,8,9,10,90,98,12,11,14,13,15,16,17+,18,29,19,20,3-9,2a,49,bc,

Fr=0,1,2,3,4,5,6,7,8,9,10,90,98,12,11,14,13,15,16,17+,18,29,19,20+,3+9,2a,4+9,bc,



Etc.



Remember: to extend F, always try the first _integer_ not yet present in F

and not leading to a contradiction. Hope my hand computed terms are ok.



Best,

É.








_______________________________________________

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