A356552 a(n) is the least base b > 1 where the sum of digits of n divides n.

2, 2, 3, 2, 5, 2, 7, 2, 3, 2, 11, 2, 13, 7, 3, 2, 17, 2, 19, 2, 2, 11, 23, 2, 3, 5, 3, 3, 29, 3, 31, 2, 3, 2, 3, 2, 37, 19, 3, 2, 41, 2, 43, 6, 3, 23, 47, 2, 7, 4, 5, 4, 53, 3, 2, 3, 3, 29, 59, 2, 61, 31, 3, 2, 3, 2, 67, 2, 2, 6, 71, 2, 73, 37, 3, 4, 3, 3, 79

Offset

1,1

Comments

This sequence is well defined: a(1) = 2, and for n > 1, the sum of digits of n in base n equals 1, which divides n.

See A356553 for the corresponding sum of digits.

Links

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

Formula

a(n) = 2 iff n belongs to A049445.

a(n) = n iff n is prime.

Example

For n = 14:
- we have:
      b   sum of digits  divides 14?
      --  -------------  -----------
       2              3  no
       3              4  no
       4              5  no
       5              6  no
       6              4  no
       7              2  yes
- so a(14) = 7.

Mathematica

a[n_] := Module[{b = 2}, While[!Divisible[n, Plus @@ IntegerDigits[n, b]], b++]; b]; Array[a, 100] (* Amiram Eldar, Aug 15 2022 *)

Prog

(PARI) a(n) = { for (b=2, oo, if (n % sumdigits(n, b)==0, return (b))) }
(Python)
from sympy.ntheory import digits
def a(n):
    b = 2
    while n != 0 and n%sum(digits(n, b)[1:]): b += 1
    return b
print([a(n) for n in range(1, 80)]) # Michael S. Branicky, Aug 12 2022

Crossrefs

Cf. A049445, A356553.

Sequence in context: A304716 A237984 A118136 * A258567 A076396 A370834

Adjacent sequences: A356549 A356550 A356551 * A356553 A356554 A356555

Keyword

nonn,base

Author

Rémy Sigrist, Aug 12 2022

Status

approved