A385116 Take the natural numbers, erase all occurrences of the digit "0," and shift all remaining digits leftward without changing the position of commas.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 21, 31, 41, 51, 61, 71, 81, 92, 21, 22, 23, 24, 25, 26, 27, 28, 29, 33, 13, 23, 33, 43, 53, 63, 73, 83, 94, 41, 42, 43, 44, 45, 46, 47, 48, 49, 55, 15, 25, 35, 45, 55, 65, 75, 85, 96, 61, 62, 63, 64, 65, 66, 67, 68, 69, 77

Offset

1,2

Comments

a(1) = 1; digit stream is the same as that of A004719 and digit lengths A055642(a(n)) = A055642(n).

Links

Dominic McCarty, Table of n, a(n) for n = 1..10000

Example

Starting with:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, ...
Erase all zeros:
1, 2, 3, 4, 5, 6, 7, 8, 9, 1_, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2_, 21, ...
Shift all remaining digits to the left:
1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 21, 31, 41, 51, 61, 71, 81, 92, 21, 22, ...

Prog

(Python)
from itertools import count
s = "".join(map(str, range(1, 72))).replace("0", "")
a, i, = [], 0
for k in count(1):
    if (j:=i+len(str(k))) > len(s): break
    a.append(int(s[i:j]))
    i = j
print(a)

Crossrefs

Cf. A004719, A055642, A032762.

Sequence in context: A355222 A033862 A329201 * A262038 A265558 A082273

Adjacent sequences: A385113 A385114 A385115 * A385117 A385118 A385119

Keyword

nonn,base,look

Author

Dominic McCarty, Jun 18 2025

Status

approved