A327664 a(n) is the least base >= 2 such that for any k in the range 0..n-1, the sum of digits of k and the sum of digits of n differ for at least one base b in the range 2..a(n).

2, 2, 3, 2, 4, 3, 3, 2, 3, 5, 4, 4, 5, 5, 3, 2, 4, 3, 5, 5, 3, 4, 4, 3, 4, 3, 3, 3, 3, 4, 3, 2, 6, 4, 4, 4, 6, 6, 6, 5, 5, 5, 4, 4, 5, 5, 3, 3, 6, 5, 6, 4, 4, 3, 5, 6, 5, 6, 6, 6, 4, 4, 3, 2, 5, 6, 5, 5, 3, 4, 5, 5, 6, 6, 5, 6, 6, 6, 3, 3, 3, 3, 5, 5, 4, 4, 4

Offset

0,1

Links

Andrew M. Johnson, Table of n, a(n) for n = 0..49999

Formula

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

a(n) <= A327667(n).

Example

For n = 9:
- the sum of digits of 9 is distinct to that of 0, 1, 2, 4, 7, 8 in base 2,
- the sum of digits of 9 equals that of 5 and 6 in base 2, but is distinct in base 3,
- the sum of digits of 9 equals that of 3 in bases 2, 3 and 4, but is distinct in base 5,
- hence a(9) = 5.

Prog

(PARI) a(n) = { my (v=2); for (k=1, n-1, for (p=2, oo, if (sumdigits(n, p)!=sumdigits(k, p), v=max(v, p); break))); return (v) }

Crossrefs

Cf. A000225, A327667.

Sequence in context: A263323 A263297 A163870 * A155043 A337327 A065770

Adjacent sequences: A327661 A327662 A327663 * A327665 A327666 A327667

Keyword

nonn,base

Author

Rémy Sigrist, Sep 21 2019

Status

approved