A086793 -id:A086793 - cp's OEIS frontend

A373092 The number of iterations of the map x -> A093653(x) that are required to reach from n to one of the fixed points, 1, 2, 3 or 6.

0, 0, 0, 1, 1, 0, 2, 2, 2, 1, 2, 3, 2, 3, 3, 2, 1, 2, 2, 3, 3, 3, 2, 4, 1, 3, 3, 4, 2, 3, 1, 1, 3, 1, 3, 4, 2, 3, 2, 4, 2, 3, 2, 4, 4, 2, 1, 4, 3, 4, 3, 4, 2, 3, 3, 3, 2, 2, 1, 4, 1, 4, 2, 3, 3, 3, 2, 3, 2, 3, 2, 4, 2, 3, 3, 4, 3, 4, 1, 4, 4, 3, 2, 4, 3, 2, 4

Offset: 1

Amiram Eldar, May 23 2024

			The iterations for the n = 1..7 are:
  n  a(n)  iterations
  -  ----  -----------
  1    0   1
  2    0   2
  3    0   3
  4    1   4 -> 3
  5    1   5 -> 3
  6    0   6
  7    2   7 -> 4 -> 3

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A086793 (decimal analog), A093653, A373093, A373094.

d[n_] := DivisorSum[n, Plus @@ IntegerDigits[#, 2] &]; a[n_] := -2 + Length@ FixedPointList[d, n]; Array[a, 100]

a(n) = {my(c = 0); while(6 % n, n = sumdiv(n, d, hammingweight(d)); c++); c;}

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

Original entry on oeis.org

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

Jason Earls, Jun 04 2004

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

Cf. A034690, A086793.

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

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

A260060 Least number such that exactly n iterations of A034690 are required to reach one of the fixed points, 1 or 15.

Original entry on oeis.org

1, 8, 7, 4, 3, 2, 19, 12, 6, 5, 13, 9, 10, 16, 30, 18, 34, 36, 66, 162, 924, 71820

Offset: 0

M. F. Hasler, Nov 08 2015

Apart from the initial term a(1), the same as A094501.

			The orbits are:
  {1},
  {8, 15},
  {7, 8, 15},
  {4, 7, 8, 15},
  {3, 4, 7, 8, 15},
  {2, 3, 4, 7, 8, 15},
  {19, 11, 3, 4, 7, 8, 15},
  {12, 19, 11, 3, 4, 7, 8, 15},
  {6, 12, 19, 11, 3, 4, 7, 8, 15},
  {5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {10, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {16, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {34, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {66, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {162, 66, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {924, 168, 102, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15},
  {71820, 1104, 168, 102, 36, 46, 18, 30, 27, 22, 9, 13, 5, 6, 12, 19, 11, 3, 4, 7, 8, 15}

E. Angelini et al., List the dividers, sum the digits, SeqFan list, Nov. 2015 [Broken link]
Eric Angelini et al., List the dividers [sic], sum the digits, lost messages reconstructed by _N. J. A. Sloane_, Dec 21 2024

Cf. A034690, A086793, A094501, A095347.

a(n)=for(k=1,9e9, A086793(k)==n&&return(k))

A094150 Number of iterations of the sum of digits of the divisors of R(n) needed to reach 15, where R(n) = A002275.

Original entry on oeis.org

5, 13, 12, 3, 11, 10, 15, 3, 14, 3, 5, 18, 13, 4, 18, 18, 5, 2, 4, 3, 12, 10, 21, 12, 18, 16, 11, 19, 20, 4, 6, 12, 13, 6, 6, 5, 3, 16, 5, 12, 12, 11, 18, 16, 18, 17, 12, 5, 12, 12, 18, 19, 14, 4, 5, 12, 18, 10, 16, 6, 13, 17, 21, 19, 6, 13, 19, 4, 3, 7, 15, 10, 21, 4, 18, 3, 5, 20, 11, 18

Offset: 2

Jason Earls, Jun 01 2004

			a(9)=3 because 111111111 -> 151 -> 8 -> 15.
a(1) does not exist because 1 -> 1 and never reaches 15.

Cf. A002275, A034690, A086793.

More terms from David Wasserman, May 22 2007

cp's OEIS Frontend

A373092 The number of iterations of the map x -> A093653(x) that are required to reach from n to one of the fixed points, 1, 2, 3 or 6.

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

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A260060 Least number such that exactly n iterations of A034690 are required to reach one of the fixed points, 1 or 15.

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PARI

A094150 Number of iterations of the sum of digits of the divisors of R(n) needed to reach 15, where R(n) = A002275.

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