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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.
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%I #9 Mar 31 2022 16:59:47

%S 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 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 5,2,7,4,4,3,5,4,4,1,8,4,4,3,7,3,2,2,6

%N 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 See A352740 for the corresponding k's.

%H 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 The first terms, alongside the corresponding k's, are:

%e n a(n) k's

%e -- ---- --------------

%e 1 1 0

%e 2 1 0

%e 3 2 0, 2

%e 4 2 0, 3

%e 5 2 0, 4

%e 6 1 0

%e 7 3 0, 4, 6

%e 8 3 0, 6, 7

%e 9 3 0, 7, 8

%e 10 2 0, 8

%e 11 5 0, 6, 8, 9, 10

%e 12 2 0, 11

%o (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 Cf. A216789, A352740.

%K nonn,base

%O 1,3

%A _Rémy Sigrist_, Mar 28 2022