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Integers whose decimal expansion start with 1, do not contain zeros and each successive digit to the right is at most one greater than the previous digit.
10

%I #22 Nov 20 2022 03:22:39

%S 1,11,12,111,112,121,122,123,1111,1112,1121,1122,1123,1211,1212,1221,

%T 1222,1223,1231,1232,1233,1234,11111,11112,11121,11122,11123,11211,

%U 11212,11221,11222,11223,11231,11232,11233,11234,12111,12112,12121

%N Integers whose decimal expansion start with 1, do not contain zeros and each successive digit to the right is at most one greater than the previous digit.

%H Robert Israel, <a href="/A071159/b071159.txt">Table of n, a(n) for n = 1..10000</a>

%H S. Giraudo, <a href="http://arxiv.org/abs/1306.6938">Combinatorial operads from monoids</a>, arXiv preprint arXiv:1306.6938 [math.CO], 2013-2015. See Sect. 3.1.3.

%p R[1]:= [1]:

%p for d from 2 to 6 do

%p R[d]:= map(t -> seq(10*t+j,j=1..min((t mod 10)+1,9)), R[d-1])

%p od:

%p A:= map(op, [seq(R[d],d=1..6)]); # _Robert Israel_, Jan 31 2017

%t desQ[n_]:=Module[{idn=IntegerDigits[n]},idn[[1]]==1&&FreeQ[idn,0]&&Max[ Differences[ idn]]<2]; Select[Range[13000],desQ] (* _Harvey P. Dale_, Feb 19 2017 *)

%Y Essentially the same as A071157 but with digits reversed.

%Y Corresponding Ɓukasiewicz words: A071153.

%K nonn,base

%O 1,2

%A _Antti Karttunen_, May 14 2002