A327667 a(n) is the least base >= 2 where n is the least number with its sum of digits.

2, 2, 3, 2, 5, 3, 7, 2, 3, 5, 11, 4, 13, 7, 5, 2, 17, 3, 19, 5, 7, 11, 23, 6, 5, 13, 3, 7, 29, 6, 31, 2, 11, 17, 7, 6, 37, 19, 13, 8, 41, 7, 43, 11, 9, 23, 47, 4, 7, 5, 17, 13, 53, 3, 11, 8, 19, 29, 59, 10, 61, 31, 9, 2, 13, 11, 67, 17, 23, 10, 71, 6, 73, 37

Offset

0,1

Links

Robert Israel, Table of n, a(n) for n = 0..10000

Formula

a(n) = 2 iff n belongs to A000225.

A327664(n) <= a(n).

a(p-1) = p for any prime number p.

Example

For n = 4:
- in base 2, 1 and 4 have the same sum of digits,
- in base 3, 2 and 4 have the same sum of digits,
- in base 4, 1 and 4 have the same sum of digits,
- in base 5, 4 is the least number with its sum of digits,
- hence a(4) = 5.

Maple

N:= 100: # for a(0)..a(N)
V:= Array(0..N):
V[0]:= 2: count:= 1:
for b from 2 while count < N+1 do
  for d from 1 to ilog[b]((N+1)/2)+2 do
    for s from (d-1)*(b-1)+1 to d*(b-1) do
      i:= s-(d-1)*(b-1);
      x:= (i+1)*b^(d-1)-1;
      if x > N then break fi;
      if V[x] = 0 then V[x]:= b; count:= count+1 fi;
od od od:
convert(V, list); # Robert Israel, Jun 27 2023

Prog

(PARI) a(n) = { for (b=2, oo, my (s=sumdigits(n, b)); if (n==((s%(b-1))+1)*b^(s\(b-1))-1, return (b))) }

Crossrefs

Cf. A000225, A327664.

Sequence in context: A051664 A318884 A280990 * A256267 A307687 A281121

Adjacent sequences: A327664 A327665 A327666 * A327668 A327669 A327670

Keyword

nonn,base,look

Author

Rémy Sigrist, Sep 21 2019

Status

approved