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A327667
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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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2
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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
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OFFSET
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0,1
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LINKS
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FORMULA
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a(p-1) = p for any prime number p.
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EXAMPLE
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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.
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MAPLE
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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:
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PROG
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(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))) }
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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