[seqfan] Re: nice base-dependent sequence

hv at crypt.org hv at crypt.org
Tue Jun 1 21:07:14 CEST 2010


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?

Hugo




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