A352671 a(n) is the number of nonnegative numbers k < n such that for any base b >= 2, the sum of digits of n and k in base b are different.

1, 1, 2, 2, 2, 1, 3, 3, 3, 2, 5, 2, 2, 3, 4, 3, 4, 3, 4, 2, 2, 1, 7, 2, 2, 3, 6, 3, 5, 1, 4, 4, 3, 3, 7, 3, 3, 3, 7, 3, 4, 1, 4, 4, 2, 2, 8, 3, 4, 4, 3, 4, 6, 4, 7, 3, 2, 1, 9, 2, 2, 3, 7, 5, 8, 3, 4, 3, 5, 2, 7, 4, 4, 3, 5, 4, 4, 1, 8, 4, 4, 3, 7, 3, 2, 2, 6

Offset

1,3

Comments

See A352740 for the corresponding k's.

Links

Table of n, a(n) for n=1..87.

Rémy Sigrist, Scatterplot of (x, y) such that x, y <= 1000 and for any base b >= 2, the sum of digits of x and y in base b are different

Example

The first terms, alongside the corresponding k's, are:
  n   a(n)  k's
  --  ----  --------------
   1     1  0
   2     1  0
   3     2  0, 2
   4     2  0, 3
   5     2  0, 4
   6     1  0
   7     3  0, 4, 6
   8     3  0, 6, 7
   9     3  0, 7, 8
  10     2  0, 8
  11     5  0, 6, 8, 9, 10
  12     2  0, 11

Prog

(PARI) a(n) = { my (v=0); for (k=0, n-1, my (ok=1); for (b=2, max(2, n+1), if (sumdigits(n, b)==sumdigits(k, b), ok=0; break)); v+=ok); v }

Crossrefs

Cf. A216789, A352740.

Sequence in context: A130267 A373687 A060610 * A351581 A017125 A063276

Adjacent sequences: A352668 A352669 A352670 * A352672 A352673 A352674

Keyword

nonn,base

Author

Rémy Sigrist, Mar 28 2022

Status

approved