My integer sequences.
These are not yet on the On-Line Encyclopedia of Internet Sequences (OEIS).
I haven't bothered to send them there, but you may do so;
you do not need permission from me and you do not have to mention me.

-------------------------------------------------------------------------------

Positive integers k such that the octal expansions of k and 2k are anagrams:
    21, 168, 189, 546, 644, 819, 1057, 1092, 1344, 1365, 1512, 1533, 1638, ...
    Example: 21 = 0o25; 2 * 21 = 0o52.
    Note: octal equivalent of A023086.
    Python program:
        print([
            k for k in range(1, 10**4)
            if sorted(format(k, "o")) == sorted(format(2 * k, "o"))
        ])

Positive integers k such that the octal expansions of k and 3k are anagrams:
    819, 882, 1134, 6552, 6643, 6916, 7042, 7056, 7154, 8050, 8302, 9072, ...
    Example: 819 = 0o1463; 3 * 819 = 0o4631.
    Note: octal equivalent of A023087.
    Python program:
        print([
            k for k in range(1, 10**4)
            if sorted(format(k, "o")) == sorted(format(3 * k, "o"))
        ])

Positive integers k such that the octal expansions of k and 4k are anagrams:
    532, 546, 819, 4116, 4130, 4228, 4256, 4326, 4354, 4368, 4508, ...
    Example: 532 = 0o1024; 4 * 532 = 0o4120.
    Note: octal equivalent of A023088.
    Python program:
        print([
            k for k in range(1, 10**4)
            if sorted(format(k, "o")) == sorted(format(4 * k, "o"))
        ])

Positive integers k such that the octal expansions of k and 5k are anagrams:
    525, 630, 735, 4109, 4200, 4725, 5033, 5040, 5110, 5558, 5880, 5887, ...
    Example: 525 = 0o1015; 5 * 525 = 0o5101.
    Note: octal equivalent of A023089.
    Python program:
        print([
            k for k in range(1, 10**4)
            if sorted(format(k, "o")) == sorted(format(5 * k, "o"))
        ])

Positive integers k such that the octal expansions of k and 6k are anagrams:
    33558, 39102, 39319, 262934, 268310, 268464, 273420, 273805, 285068, ...
    Example: 33558 = 0o101426; 6 * 33558 = 0o611204.
    Note: octal equivalent of A023090.
    Python program:
        print([
            k for k in range(1, 10**6)
            if sorted(format(k, "o")) == sorted(format(6 * k, "o"))
        ])

Positive integers k such that the octal expansions of k and 7k are anagrams:
    567, 4151, 4319, 4536, 4543, 4599, 32823, 32991, 33208, 33215, ...
    Example: 567 = 0o1067; 7 * 567 = 0o7601.
    Notes: octal equivalent of A023091.
    Python program:
        print([
            k for k in range(1, 10**6)
            if sorted(format(k, "o")) == sorted(format(7 * k, "o"))
        ])

a(n) is the smallest positive integer k such that the octal expansions of k and
nk are anagrams:
    1, 21, 819, 532, 525, 33558, 567
    Example: a(3) = 819 because 819 = 0o1463 and 3 * 819 = 0o4631.
    Notes: finite; octal equivalent of A133220.
    Python program:
        for n in range(1, 7 + 1):
            for k in range(1, 10**6):
                if sorted(format(k, "o")) == sorted(format(n * k, "o")):
                    print(k)
                    break

Numbers k whose octal expansion can be permuted to produce the octal expansion
of a multiple of k:
    21, 168, 189, 525, 532, 546, 567, 630, 644, 735, 819, 882, ...
    Example: 21 = 0o25; 2 * 21 = 0o52.
    Note: octal equivalent of A245680.
    Python program:
        print([
            k for k in range(1, 1000) if any(
                sorted(format(k, "o")) == sorted(format(m * k, "o"))
                for m in range(2, 7 + 1)
            )
        ])

-------------------------------------------------------------------------------
Back to Qalle's home page: https://qalle.neocities.org