A001073 Label a 1-cm ruler with digits 1 cm wide.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 2, 1, 4, 1, 6, 1, 8, 2, 0, 2, 2, 2, 4, 2, 6, 2, 8, 3, 0, 3, 2, 3, 4, 3, 6, 3, 8, 4, 0, 4, 2, 4, 4, 4, 6, 4, 8, 5, 0, 5, 2, 5, 4, 5, 6, 5, 8, 6, 0, 6, 2, 6, 4, 6, 6, 6, 8, 7, 0, 7, 2, 7, 4, 7, 6, 7, 8, 8, 0, 8, 2, 8, 4, 8, 6, 8, 8, 9, 0, 9, 2, 9, 4, 9, 6, 9, 8, 1, 0, 0, 1, 0, 3

Offset

0,3

Comments

The initial cm 0-9 can each be labeled because the labels take up one cm each, but the label for cm 10 takes up 2 cm, so cm 11 does not have its own label. Now 12 is labeled. This continues until cm 100 is labeled, which takes up 3 spaces, so 101 and 102 do not have their own label. - John Cerkan, Feb 14 2017

Or, let a'(n) be the length of all previous numbers in a(n), concatenated, then a(n) is a list of all the digits of each term of a'(n). - John Cerkan, Feb 16 2017

This sequence corresponds to the decimal digits of the terms of A088235. - Rémy Sigrist, Sep 25 2021

Links

John Cerkan, Table of n, a(n) for n = 0..10000

Mathematica

nmax = 105; f[0] = 0; f[n_] := f[n] = f[n-1] + Length[IntegerDigits[f[n-1]]]; digits = Table[IntegerDigits[f[n]], {n, 0, nmax}] // Flatten; a[n_] := digits[[n+1]]; Table[a[n], {n, 0, nmax}] (* Jean-François Alcover, Nov 26 2013 *)

Prog

(Python)
from itertools import islice
def agen():
    an = 0
    while True: s = str(an); yield from map(int, s); an += len(s)
print(list(islice(agen(), 67))) # Michael S. Branicky, Jul 26 2022

Crossrefs

Cf. A088235.

Sequence in context: A007376 A189823 A325479 * A274580 A241494 A076313

Adjacent sequences: A001070 A001071 A001072 * A001074 A001075 A001076

Keyword

nonn,base,nice

Author

R. Lozyniak (11(AT)onna.com)

Status

approved