A340490 a(n) is the number of digits after the n-th digit of the Champernowne constant A033307 until the next appearance of that digit.

9, 13, 14, 15, 16, 17, 18, 19, 20, 2, 20, 1, 1, 2, 15, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 5, 20, 2, 20, 2, 20, 1, 1, 2, 13, 2, 20, 2, 20, 2, 20, 2, 20, 2, 20, 7, 20, 2, 20, 2, 20, 2, 20, 1, 1, 2, 11, 2, 20, 2, 20, 2, 20, 2, 20, 9, 20, 2, 20, 2, 20, 2

Offset: 1

Author

Md. Towhidul Islam, Jan 10 2021

Keywords

• nonn
• base

Comments

In typing the positive integers without leaving spaces between them, it is interesting to see how many places later we press the same number key on the keyboard. This sequence answers that question.

Examples

			In concatenating the positive integers, we get 1 first. The next occurrence of 1 is in 10. So 1 occurs 9 places later, which gives a(1)=9. The second digit 2 occurs again in writing 12. So 2 occurs 13 places later and a(2) is 13.
		

Links

• Md. Towhidul Islam, Table of n, a(n) for n = 1..31968

Crossrefs

Cf. A033307 (the parent sequence).

Programs

PARI

C(nn) = {my(list = List()); for (n=1, nn, my(d=digits(n)); for (k=1, #d, listput(list, d[k]););); list;} \\ A033307
posi(list, i) = {for (j=i+1, #list, if (list[i] == list[j], return (j-i)););}
lista(nn) = {my(list = C(nn)); my(listp = List()); for (i=1, #list, my(pos = posi(list, i)); if (! pos, break); listput(listp, pos);); Vec(listp);} \\ Michel Marcus, Jan 11 2021

Python

def aupton(terms):
    alst, chapnk, k = [], [1], 1
    for n in range(1, terms+1):
        chapn = chapnk.pop(0)
        while chapn not in chapnk:
            k += 1
            chapnk.extend(list(map(int, str(k))))
        alst.append(chapnk.index(chapn) + 1)
    return alst
print(aupton(74)) # Michael S. Branicky, Sep 13 2021

Formula

A033307(n - 1 + a(n)) = A033307(n - 1).