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

Author

Rémy Sigrist, Mar 28 2022

Keywords

• nonn
• base

Comments

See A352740 for the corresponding k's.

Examples

			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
		

Links

• 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

Crossrefs

Cf. A216789, A352740.

Programs

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 }