A348192 - OEIS

%I #41 Jun 02 2025 15:24:38

%S 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,

%T 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,

%U 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

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

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

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

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

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

%o (Python)

%o from itertools import count, islice

%o from math import gcd

%o def A348192_gen(): # generator of terms

%o     blist = [0]

%o     yield 0

%o     for n in count(1):

%o         blist.append(1+blist[n-gcd(n,sum(int(d) for d in str(n)))])

%o         yield blist[-1]

%o A348192_list = list(islice(A348192_gen(),30)) # _Chai Wah Wu_, Jan 26 2022

%Y Cf. A007953, A066750.

%K nonn,base

%O 0,11

%A _Ctibor O. Zizka_, Jan 25 2022