A360656 Least k such that the decimal representation of 2^k contains all possible n-digit strings.

68, 975, 16963, 239697, 2994863

Offset: 1

Author

Hans Havermann, Feb 15 2023

Keywords

• nonn
• base
• more

Examples

			2^68 = 295147905179352825856 is the least power of 2 containing all ten decimal digits, so a(1) = 68 = A171744(1).
2^975 is the least power of 2 containing all 100 two-digit strings, so a(2) = 975.
		

Crossrefs

Cf. A171744, A360623.

Programs

Python

def a(n, starte=0):
    e, p2, t = starte, 2**starte, 10**n
    while True:
        s2, ss = str(p2), set()
        for i in range(len(s2)-n+1):
            ss.add(s2[i:i+n])
            if len(ss) == t:
                return e
        e += 1
        p2 *= 2
print([a(n) for n in range(1, 4)]) # Michael S. Branicky, Feb 22 2023