A364325 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.

1, 10, 20, 22, 200, 220, 221, 222, 201, 202, 223, 224, 203, 225, 226, 11, 227, 228, 229, 302, 204, 12, 312, 205, 322, 332, 342, 23, 352, 362, 24, 372, 206, 230, 382, 392, 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

Offset

1,2

Links

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

Example

The leftmost digit of a(1) = 1 is 1: this digit underlines the 1st digit of a(1) which is (1);
The leftmost digit of a(2) = 10 is 1: this digit underlines the 1st digit of a(2) which is (1);
The leftmost digit of a(3) = 20 is 2: this digit underlines the 2nd digit of a(3) which is (0);
The leftmost digit of a(4) = 22 is 2: this digit underlines the 2nd digit of a(4) which is (2);
The leftmost digit of a(5) = 200 is 2: this digit underlines the 2nd digit of a(5) which is (0);
The leftmost digit of a(6) = 220 is 2: this digit underlines the 2nd digit of a(6) which is (2); 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=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 *)

Prog

(Python)
from itertools import count, filterfalse
def check(x):
    y = str(x)
    if int(y[0])> len(y): return(True)
def A364325_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[0])-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. A364326.

Sequence in context: A325198 A098165 A104801 * A144140 A361337 A034048

Adjacent sequences: A364322 A364323 A364324 * A364326 A364327 A364328

Keyword

base,nonn

Author

Eric Angelini, Jul 18 2023

Status

approved