cp's OEIS Frontend

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.

%I A352671 #9 Mar 31 2022 16:59:47
%S A352671 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,
%T A352671 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,
%U A352671 5,2,7,4,4,3,5,4,4,1,8,4,4,3,7,3,2,2,6
%N 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.
%C A352671 See A352740 for the corresponding k's.
%H A352671 Rémy Sigrist, <a href="/A352671/a352671.png">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</a>
%e A352671 The first terms, alongside the corresponding k's, are:
%e A352671   n   a(n)  k's
%e A352671   --  ----  --------------
%e A352671    1     1  0
%e A352671    2     1  0
%e A352671    3     2  0, 2
%e A352671    4     2  0, 3
%e A352671    5     2  0, 4
%e A352671    6     1  0
%e A352671    7     3  0, 4, 6
%e A352671    8     3  0, 6, 7
%e A352671    9     3  0, 7, 8
%e A352671   10     2  0, 8
%e A352671   11     5  0, 6, 8, 9, 10
%e A352671   12     2  0, 11
%o A352671 (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 }
%Y A352671 Cf. A216789, A352740.
%K A352671 nonn,base
%O A352671 1,3
%A A352671 _Rémy Sigrist_, Mar 28 2022