%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 kth 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@kf==0,True, If[IntegerDigits[k][[f]]!=Flatten[IntegerDigits/@Join[Array[a,n1],{k}]][[n]],True]]MemberQ[Array[a,n1],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
