A348192 a(0) = 0; for n >= 1, a(n) = 1 + a(n - GCD(n, digital sum(n)))

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 2, 3, 4, 3, 4, 5, 2, 3, 3, 3, 4, 5, 3, 4, 4, 3, 5, 6, 4, 5, 6, 5, 6, 7, 4, 5, 6, 5, 5, 6, 5, 6, 6, 5, 7, 8, 5, 6, 6, 6, 7, 8, 6, 7, 8, 7, 8, 9, 7, 8, 8, 7, 9, 10, 8, 9, 9, 9, 8, 9, 8, 9, 10, 9, 10, 9, 10, 11, 9, 9, 10, 11, 9, 10, 10, 10, 10, 11, 10, 11, 12, 11, 12, 13, 12, 13

Offset

0,11

Comments

Number of steps needed to reach zero when starting from k = n and repeatedly applying the map that replaces k by k - A066750(k).

Links

Table of n, a(n) for n=0..97.

Formula

a(0) = 0; for n >= 1, a(n) = 1 + a(n - A066750(n)).

Example

n = 12, a(12) = 1 + a(12 - GCD(12,3)) = 1 + a(9) = 1 + 1 + a(9 - GCD(9,9)) = 2 + a(0) = 2.

Mathematica

a[0] = 0; a[n_] := a[n] = 1 + a[n - GCD[n, Plus @@ IntegerDigits[n]]]; Array[a, 100, 0] (* Amiram Eldar, Jan 25 2022 *)

Prog

(Python)
from itertools import count, islice
from math import gcd
def A348192_gen(): # generator of terms
    blist = [0]
    yield 0
    for n in count(1):
        blist.append(1+blist[n-gcd(n, sum(int(d) for d in str(n)))])
        yield blist[-1]
A348192_list = list(islice(A348192_gen(), 30)) # Chai Wah Wu, Jan 26 2022

Crossrefs

Cf. A007953, A066750.

Sequence in context: A156723 A240834 A256993 * A173523 A199323 A156549

Adjacent sequences: A348189 A348190 A348191 * A348193 A348194 A348195

Keyword

nonn,base

Author

Ctibor O. Zizka, Jan 25 2022

Status

approved