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%I #30 Oct 23 2023 18:53:05
%S 1,10,20,22,200,220,221,222,201,202,223,224,203,225,226,11,227,228,
%T 229,302,204,12,312,205,322,332,342,23,352,362,24,372,206,230,382,392,
%U 25,2200,2201,26,13,14,2202,2203,27,2204,2205,28,2206,2207,29,231,207,2208,2209,208,240,15,2210,232,16,2211
%N Underline the k-th digit of a(n), k being the leftmost digit of a(n). This is the lexicographically earliest sequence of distinct terms > 0 such that the succession of underlined digits is the succession of the sequence's digits themselves.
%H John Tyler Rascoe, <a href="/A364325/b364325.txt">Table of n, a(n) for n = 1..10000</a>
%e The leftmost digit of a(1) = 1 is 1: this digit underlines the 1st digit of a(1) which is (1);
%e The leftmost digit of a(2) = 10 is 1: this digit underlines the 1st digit of a(2) which is (1);
%e The leftmost digit of a(3) = 20 is 2: this digit underlines the 2nd digit of a(3) which is (0);
%e The leftmost digit of a(4) = 22 is 2: this digit underlines the 2nd digit of a(4) which is (2);
%e The leftmost digit of a(5) = 200 is 2: this digit underlines the 2nd digit of a(5) which is (0);
%e The leftmost digit of a(6) = 220 is 2: this digit underlines the 2nd digit of a(6) which is (2); 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=First@IntegerDigits[k])>IntegerLength@k,True, If[IntegerDigits[k][[f]]!=Flatten[IntegerDigits/@Join[Array[a,n-1],{k}]][[n]]||MemberQ[Array[a,n-1],k],True]],k++];k);Array[a,70] (* _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[0])> len(y): return(True)
%o def A364325_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[0])-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. A364326.
%K base,nonn
%O 1,2
%A _Eric Angelini_, Jul 18 2023
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