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

Author

Ctibor O. Zizka, Jan 25 2022

Keywords

• nonn
• base

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).

Examples

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

Crossrefs

Cf. A007953, A066750.

Programs

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 *)

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

Formula

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