A309417 Number of steps needed to reduce 10^n to zero by subtracting its digital sum.

2, 11, 81, 611, 4798, 39320, 333583, 2897573, 25632474, 230231687, 2091437006, 19145032382, 176258021378, 1630867803755, 15161044498785, 141573907590908, 1327916557473475, 12513166293358138, 118472791400037286, 1126683083504083356, 10754171449735292485

Offset: 1

Author

Reiner Moewald, Jul 30 2019

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• Dominic McCarty, Table of n, a(n) for n = 1..500
• Dominic McCarty, Python program for A309417

Crossrefs

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

Programs

Mathematica

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

PARI

a(n)={my(s=10^n, k=0); while(s, k++; s-=sumdigits(s)); k} \\ Andrew Howroyd, Sep 09 2019

Python

import math
def digitsum(n):
   ds = 0
   while n > 0:
      ds += n % 10
      n = n // 10
   return ds
def steps(n):
   count = 0
   while n > 0:
      n = n - digitsum(n)
      count += 1
   return count
n = 1
for i in range(1,10):
   n = 10 * n
   print(steps(n))

Extensions

a(13)-a(15) from Giovanni Resta, Sep 10 2019

a(16) and on from Dominic McCarty, Feb 12 2025