[seqfan] Re: nice base-dependent sequence

[hv at crypt.org]

hv at crypt.org wrote:
:I started looking at this, but didn't realise until after I had written
:the program that I had misinterpreted the definition - I was looking only
:at the left-anchored substrings, not at all substrings, so what I have
:actually calculated is the sequence:
:  Smallest integer k such that k or one of its left substrings (regarded as an
:  integer) is divisible by any integer from {1,2,...,n}
:Or more formally:
:  a(n) = min m: forall d in {1..n}: exists k in {0..log_10(m)}:
:    d | floor(m / 10^k)
:
:If I've calculated correctly, initial values of this sequence are:
:a(1..10): 1, 2, 6, 12, 45, 60, 245, 245, 504, 504,
:a(11..20): 5049, 5049, 10296, 11760, 11760, 11760, 56160, 56160, 198016, 198016,
:a(21..30): 781286, 1323008, 2340849, 6240366, 13442580, 13442580, 22680329,
:  25380966, 75432065, 75432065,
:a(31..40): 180092645, 319800096, 319800096, 800640126, 2046241575, 2201169600,
:  3780487275, 5250966084, 5250966084, 6832425609
:
:Is this additionally worth submitting?

My domain had expired, but is now renewed. If anyone sent a private reply
to this, please resend it. Apologies for any inconvenience.

Additional comments: one reason I think why I made the mistake I did is
because subconsciously I knew that allowing all substrings would break as
soon as a candidate had a zero-digit embedded.

I think the original sequence needs an additional proviso for this, else
that sequence will boringly go "1, 2, 6, 10, 10, 10, ...".

It has also occurred to me I should use the word "prefix" above rather
than "left substring".

Hugo