A364326 - OEIS

%I #18 Oct 23 2023 18:53:30

%S 1,11,101,111,102,112,121,131,141,151,202,12,161,171,21,181,22,191,

%T 212,31,312,412,41,512,612,51,712,32,302,42,812,52,912,61,1001,1011,

%U 71,1013,62,1021,1031,81,1041,72,82,1051,91,1061,92,1071,122,103,1081,113,1091,201,142,1101,211,242

%N Underline the k-th digit of a(n), k being the rightmost digit of a(n). This is the lexicographically earliest sequence of distinct terms > 0 such that the succession of the underlined digit is the succession of the sequence's digits themselves.

%H John Tyler Rascoe, <a href="/A364326/b364326.txt">Table of n, a(n) for n = 1..10000</a>

%e The rightmost digit of a(1) = 1 is 1: this digit underlines the 1st digit of a(1) which is (1);

%e The rightmost digit of a(2) = 11 is 1: this digit underlines the 1st digit of a(2) which is (1);

%e The rightmost digit of a(3) = 101 is 1: this digit underlines the 1st digit of a(3) which is (1);

%e The rightmost digit of a(4) = 111 is 1: this digit underlines the 1st digit of a(4) which is (1);

%e The rightmost digit of a(5) = 102 is 2: this digit underlines the 2nd digit of a(5) which is (0);

%e The rightmost digit of a(6) = 112 is 2: this digit underlines the 2nd digit of a(6) which is (1); etc.

%e We see that the parenthesized digits at the end of each line reproduce the succession of the original digits.

%t a[1]=1;a[n_]:=a[n]=(k=1;While[If[(f=Mod[k,10])>IntegerLength@k||f==0,True, If[IntegerDigits[k][[f]]!=Flatten[IntegerDigits/@Join[Array[a,n-1],{k}]][[n]],True]]||MemberQ[Array[a,n-1],k],k++];k);Array[a,60] (* _Giorgos Kalogeropoulos_, Jul 19 2023 *)

%o (Python)

%o from itertools import count, filterfalse

%o def check(x):

%o     y = str(x)

%o     if int(y[-1])> len(y) or y[-1] == '0': return(True)

%o def A364326_list(max_n):

%o     A,S,Z,zx = [],set(),'',0

%o     for n in range(1,max_n+1):

%o         for i in filterfalse(S.__contains__, count(1)):

%o             if check(i): S.add(i)

%o             else:

%o                 x = str(i)

%o                 u = x[int(x[-1])-1]

%o                 if len(Z) == zx and u == x[0]: break

%o                 elif u == Z[zx]: break

%o         A.append(i); S.add(i); Z += x; zx += 1

%o     return(A) # _John Tyler Rascoe_, Oct 23 2023

%Y Cf. A364325.

%K base,nonn

%O 1,2

%A _Eric Angelini_, Jul 18 2023