[seqfan] First "stringed" sequence as a whole

[Eric Angelini]

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.