cp's OEIS Frontend

A370678 a(n) is the number of pairs x <= y of n-digit numbers such that the number of distinct digits in their product is less than in their concatenation.

%I A370678 #18 Feb 29 2024 13:01:36
%S A370678 10,1395,147718,15187437,1530456465,152653821364
%N A370678 a(n) is the number of pairs x <= y of n-digit numbers such that the number of distinct digits in their product is less than in their concatenation.
%F A370678 a(n) = 9 * 2^(n-3) * 5^(n-2) * (10 + 9*10^n) - A370679(n) - A370680(n).
%e A370678 a(1) = 10: 8 products 1*2, ..., 1*9, 2*3, 2*4 with 1 digit in x*y and 2 digits in x|y.
%o A370678 (PARI) \\ returns [number of products, [a(n), A370679(n), A370680(n)]]
%o A370678  a370678_80(n) = {my (m=0, c=vector(3), n1=10^(n-1), n2=10*n1-1); for (k1=n1, n2, my (s1=digits(k1)); for (k2=k1, n2, my (s2=digits(k2), cs=#Set(digits(k1*k2)), d=cs-#Set(concat(s1,s2))); c[sign(d)+2]++; m++)); [m,c]}
%o A370678 (Python)
%o A370678 def A370678(n):
%o A370678     a = 10**(n-1)
%o A370678     b, c = 10*a, 0
%o A370678     for x in range(a,b):
%o A370678         s = set(str(x))
%o A370678         for y in range(x,b):
%o A370678             if len(s|set(str(y))) > len(set(str(x*y))):
%o A370678                 c += 1
%o A370678     return c # _Chai Wah Wu_, Feb 28 2024
%Y A370678 Cf. A370675, A370676, A370679, A370680.
%K A370678 nonn,base,more
%O A370678 1,1
%A A370678 _Hugo Pfoertner_, Feb 26 2024
%E A370678 a(6) from _Martin Ehrenstein_, Feb 29 2024