A364326 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.

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

Offset

1,2

Links

John Tyler Rascoe, Table of n, a(n) for n = 1..10000

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@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 *)

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)
def A364326_list(max_n):
    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
    return(A) # John Tyler Rascoe, Oct 23 2023

Crossrefs

Cf. A364325.

Sequence in context: A278937 A038444 A115824 * A208259 A043036 A072001

Adjacent sequences: A364323 A364324 A364325 * A364327 A364328 A364329

Keyword

base,nonn

Author

Eric Angelini, Jul 18 2023

Status

approved