A309417 - OEIS

%I #28 Sep 23 2019 14:14:15

%S 2,11,81,611,4798,39320,333583,2897573,25632474,230231687,2091437006,

%T 19145032382,176258021378,1630867803755,15161044498785

%N Number of steps needed to reduce 10^n to zero by subtracting its digital sum.

%C Conjecture: lim_{n->infinity} a(n+1)/a(n) = 10.

%e a(100)=11 since 100->99->81->72->63->54->45->36->27->18->9->0.

%t f[n_] := Length[NestWhileList[# - Total[IntegerDigits[#]]&, n, # > 0 &]]-1; f /@ (10^Range[8]) (* _Amiram Eldar_, Aug 08 2019 *)

%o (Python)

%o import math

%o def digitsum(n):

%o    ds = 0

%o    while n > 0:

%o       ds += n % 10

%o       n = n // 10

%o    return ds

%o def steps(n):

%o    count = 0

%o    while n > 0:

%o       n = n - digitsum(n)

%o       count += 1

%o    return count

%o n = 1

%o for i in range(1,10):

%o    n = 10 * n

%o    print(steps(n))

%o (PARI) a(n)={my(s=10^n, k=0); while(s, k++; s-=sumdigits(s)); k} \\ _Andrew Howroyd_, Sep 09 2019

%Y Cf. A066568 (n - sum of digits of n).

%K nonn,base,more

%O 1,1

%A _Reiner Moewald_, Jul 30 2019

%E a(13)-a(15) from _Giovanni Resta_, Sep 10 2019