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A298372 a(n), in decimal base, is the number of numbers k >= 0 with no more digits than n such that k + n can be computed without carry.

%I A298372 #16 Jan 22 2018 03:05:22
%S A298372 1,9,8,7,6,5,4,3,2,1,90,81,72,63,54,45,36,27,18,9,80,72,64,56,48,40,
%T A298372 32,24,16,8,70,63,56,49,42,35,28,21,14,7,60,54,48,42,36,30,24,18,12,6,
%U A298372 50,45,40,35,30,25,20,15,10,5,40,36,32,28,24,20,16,12,8
%N A298372 a(n), in decimal base, is the number of numbers k >= 0 with no more digits than n such that k + n can be computed without carry.
%C A298372 We consider here that 0 has no digit, and hence a(0) = 1.
%C A298372 The corresponding sequence for the binary base is A080100.
%H A298372 Rémy Sigrist, <a href="/A298372/b298372.txt">Table of n, a(n) for n = 0..9999</a>
%F A298372 a(0) = 1.
%F A298372 a(10 * k + d) = a(k) * (10 - d) when 10 * k + d > 0 and 0 <= d < 10.
%F A298372 a(n) = Product_{ d = 0..9 } (10 - d)^A100910(n, d) for any n > 0.
%e A298372 a(42) = (10 - 4) * (10 - 2) = 48.
%o A298372 (PARI) a(n, {base=10}) = my (d=digits(n, base)); prod(i=1, #d, base-d[i])
%Y A298372 Cf. A080100, A100910.
%K A298372 nonn,base
%O A298372 0,2
%A A298372 _Rémy Sigrist_, Jan 18 2018