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

1,1

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.

Links

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

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A033307 (the parent sequence).

Sequence in context: A050236 A193995 A070607 * A335662 A191891 A135439

Adjacent sequences: A340487 A340488 A340489 * A340491 A340492 A340493

Keyword

nonn,base

Author

Md. Towhidul Islam, Jan 10 2021

Status

approved