A094450 Number of iterations of the sum of digits of the divisors of 10^n needed to reach 15.

12, 10, 16, 15, 3, 11, 4, 13, 6, 6, 5, 19, 16, 3, 11, 13, 19, 7, 5, 9, 6, 16, 16, 19, 5, 3, 12, 3, 18, 16, 4, 10, 6, 16, 18, 12, 4, 16, 12, 13, 12, 5, 12, 5, 20, 15, 16, 12, 4, 16, 4, 20, 5, 19, 4, 6, 21, 5, 6, 5, 21, 12, 5, 16, 13, 17, 6, 5, 7, 21, 20, 18, 12, 10, 6, 18, 13, 13, 6, 13, 15

Offset: 1

Author

Jason Earls, Jun 04 2004

Keywords

• base
• nonn

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1400

Crossrefs

Cf. A034690, A086793.

Programs

Mathematica

Table[Length[NestWhileList[Total[Flatten[IntegerDigits/@Divisors[#]]]&,10^n, #!= 15&]]-1,{n,90}] (* Harvey P. Dale, Mar 05 2019 *)

Python

from sympy import divisors
def sd(n): return sum(map(int, str(n)))
def f(n): return sum(sd(d) for d in divisors(n, generator=True))
def a(n):
    i, c = 10**n, 0
    while i != 15: i = f(i); c += 1
    return c
print([a(n) for n in range(1, 82)]) # Michael S. Branicky, Dec 10 2021