

A364326


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.


2



1, 11, 101, 111, 102, 112, 121, 131, 141, 151, 202, 12, 161, 171, 21, 181, 22, 191, 212, 31, 312, 412, 41, 512, 612, 51, 712, 32, 302, 42, 812, 52, 912, 61, 1001, 1011, 71, 1013, 62, 1021, 1031, 81, 1041, 72, 82, 1051, 91, 1061, 92, 1071, 122, 103, 1081, 113, 1091, 201, 142, 1101, 211, 242
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OFFSET

1,2


LINKS



EXAMPLE

The rightmost digit of a(1) = 1 is 1: this digit underlines the 1st digit of a(1) which is (1);
The rightmost digit of a(2) = 11 is 1: this digit underlines the 1st digit of a(2) which is (1);
The rightmost digit of a(3) = 101 is 1: this digit underlines the 1st digit of a(3) which is (1);
The rightmost digit of a(4) = 111 is 1: this digit underlines the 1st digit of a(4) which is (1);
The rightmost digit of a(5) = 102 is 2: this digit underlines the 2nd digit of a(5) which is (0);
The rightmost digit of a(6) = 112 is 2: this digit underlines the 2nd digit of a(6) which is (1); etc.
We see that the parenthesized digits at the end of each line reproduce the succession of the original digits.


MATHEMATICA

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 *)


PROG

(Python)
from itertools import count, filterfalse
def check(x):
y = str(x)
if int(y[1])> len(y) or y[1] == '0': return(True)
A, S, Z, zx = [], set(), '', 0
for n in range(1, max_n+1):
for i in filterfalse(S.__contains__, count(1)):
if check(i): S.add(i)
else:
x = str(i)
u = x[int(x[1])1]
if len(Z) == zx and u == x[0]: break
elif u == Z[zx]: break
A.append(i); S.add(i); Z += x; zx += 1


CROSSREFS



KEYWORD

base,nonn


AUTHOR



STATUS

approved



