A370680 a(n) is the number of pairs x <= y of n-digit numbers such that the number of distinct digits in their product is greater than in their concatenation.

6, 1026, 120878, 13234670, 1383218064, 140953635171

Offset: 1

Author

Hugo Pfoertner, Feb 26 2024

Keywords

• nonn
• base
• more

Examples

			a(1) = 6: 6 squares 4*4, ..., 9*9 with 2 distinct digits in x*y = 16, 25, ..., and 1 digit in their concatenation.
		

Crossrefs

Cf. A370675, A370676, A370678, A370679.

Programs

PARI

See A370678.

Python

def A370680(n):
    a = 10**(n-1)
    b, c = 10*a, 0
    for x in range(a,b):
        s = set(str(x))
        for y in range(x,b):
            if len(s|set(str(y))) < len(set(str(x*y))):
                c += 1
    return c # Chai Wah Wu, Feb 28 2024

Extensions

a(6) from Martin Ehrenstein, Feb 29 2024