A175516 a(n) = smallest positive even integer k such that k or one of its left substrings is divisible by any integer from {1..n}.

2, 2, 6, 12, 60, 60, 252, 504, 504, 504, 7260, 7260, 10296, 11760, 11760, 11760, 56160, 56160, 198016, 198016, 1176480, 1323008, 2992500, 6240366, 13442580, 13442580, 37536408, 37536408, 90725804, 90725804, 319800096, 319800096, 319800096, 800640126, 2201169600, 2201169600, 4656965040, 5250966084, 5250966084

Offset: 1

Author

Zak Seidov, Jun 03 2010

Keywords

• base
• nonn

Links

• Hugo van der Sanden, A169858: C source code to calculate terms (has an option to compute A175516).

Crossrefs

Cf. A169858.

Programs

Python

from itertools import count, islice
def agen(): # generator of terms
    n = 1
    for k in count(2, 2):
        s = str(k)
        prefixes = [int(s[:i+1]) for i in range(len(s))]
        if all(any(ki%m == 0 for ki in prefixes) for m in range(3, n+1)):
            yield k; n += 1
            while any(ki%n == 0 for ki in prefixes):
                yield k; n += 1
print(list(islice(agen(), 20))) # Michael S. Branicky, Jun 09 2023

Extensions

Corrected and extended by Hugo van der Sanden, Jun 01 2010