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a(n) is the least base >= 2 where n is the least number with its sum of digits.
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%I #12 Jun 27 2023 17:44:08

%S 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,

%T 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,

%U 19,29,59,10,61,31,9,2,13,11,67,17,23,10,71,6,73,37

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

%H Robert Israel, <a href="/A327667/b327667.txt">Table of n, a(n) for n = 0..10000</a>

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

%F A327664(n) <= a(n).

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

%e For n = 4:

%e - in base 2, 1 and 4 have the same sum of digits,

%e - in base 3, 2 and 4 have the same sum of digits,

%e - in base 4, 1 and 4 have the same sum of digits,

%e - in base 5, 4 is the least number with its sum of digits,

%e - hence a(4) = 5.

%p N:= 100: # for a(0)..a(N)

%p V:= Array(0..N):

%p V[0]:= 2: count:= 1:

%p for b from 2 while count < N+1 do

%p for d from 1 to ilog[b]((N+1)/2)+2 do

%p for s from (d-1)*(b-1)+1 to d*(b-1) do

%p i:= s-(d-1)*(b-1);

%p x:= (i+1)*b^(d-1)-1;

%p if x > N then break fi;

%p if V[x] = 0 then V[x]:= b; count:= count+1 fi;

%p od od od:

%p convert(V,list); # _Robert Israel_, Jun 27 2023

%o (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))) }

%Y Cf. A000225, A327664.

%K nonn,base,look

%O 0,1

%A _Rémy Sigrist_, Sep 21 2019