A395985 Smallest base such that n is a repunit in that base.

2, 3, 4, 5, 2, 7, 8, 9, 10, 11, 3, 13, 2, 15, 16, 17, 18, 19, 4, 21, 22, 23, 24, 25, 26, 27, 28, 29, 2, 31, 32, 33, 34, 35, 36, 37, 38, 3, 40, 41, 6, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 7, 57, 58, 59, 60, 61, 2, 63, 64, 65, 66, 67, 68, 69, 70, 71, 8, 73, 74, 75

Offset

3,1

Comments

1<a(n)<n.

When A088323(n)=1, a(n)=n-1.

When A088323(n)>1, a(n)<n-1.

Links

Mital Ashok, Table of n, a(n) for n = 3..10000

Example

For n = 7, a(7) = 2 because 7 is 111_2 in base 2.

Maple

f:= proc(n) local b, t;
    for b from 2 to floor(sqrt(n)) do
      t:= n*(b-1)+1;
      if t = b^padic:-ordp(t, b) then return b fi
    od;
    n-1
end proc:
map(f, [$3..100]); # Robert Israel, May 17 2026

Mathematica

a[n_]:=Module[{b=1}, Until[ContainsOnly[IntegerDigits[n, b], {1}], b++]; b]; Array[a, 74, 3] (* James C. McMahon, May 17 2026 *)

Prog

(Python)
def a(n):
  for b in range(2, n):
    x = (b-1)*n+1
    while x%b == 0:
      x //= b
    if x == 1:
      return b
(Python)
from itertools import count
from sympy import integer_log
def A395985(n): return next(filter(lambda b: integer_log(n*(b-1)+1, b)[1], count(2))) # Chai Wah Wu, May 17 2026

Crossrefs

Cf. A088323, A055129.

Sequence in context: A162961 A145255 A344758 * A053626 A348990 A348968

Adjacent sequences: A395982 A395983 A395984 * A395986 A395987 A395988

Keyword

nonn,base

Author

Mital Ashok, May 13 2026

Status

approved