[seqfan] 8 seq. [from digits d<e<f to d>=e>=f]

[Eric Angelini]

Hello SeqFans,
We want a seq. S of terms a(n) such that:
1) a(1)=1
2) any three consecutive digits d, e and f of S don't show d<e<f
3) S is extended with the smallest integer not yet present in S.

I guess S starts like this:

S=1,2,10,3,11,4,12,13,14,15,5,6,16,17,7,8,18,19,20,
21-->120,200,201,121,122,130,202,131,132,133,140,
203,141,142,143,144,150,204,151,152,153,154,155,
160,205,...

[21-->120, above, meaning "all integers from 21 to 120"]

Playing with the signs <,=,> to be put between d, e and f,
one could compute the sequences T to Z with:
T ... d<=e<f
U ... d<e<=f
V ... d<=e<=f
W ... d>e>f
X ... d>=e>f
Y ... d>e>=f
Z ... d>=e>=f

Best,
É.