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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. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
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
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Jul 18 2023
STATUS
approved

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Last modified May 26 10:56 EDT 2024. Contains 372824 sequences. (Running on oeis4.)