In case you're interested, here are the sequences for base 11 and base 13: 20 sequences of length 11 ["379061A4258","3791A425806","425067391A8","4251A806739","4251A873906","58061A42379","581A4237906", "603791A4258","604251A8739","60581A42379","609371A4258","609573241A8","61A42379058","61A42580379", "61A42580937","673904251A8","67391A80425","937061A4258","9371A425806","9573241A806"] 0 sequences of length 12 18 sequences of length 13 ["315C0926A48B7","31907B26A485C","348B70926A15C","348B715C0926A","5BA862170C439","5BA8621C43907", "5C26A4831B709","705BA8621C439","7B26A485C0319","905C26A4831B7","926A0348B715C","926A15C0348B7", "926A48B70315C","9CB5843170A26","A2609CB584317","B0C6298A43157","C43905BA86217","C6298A431570B"] On Sun, Mar 4, 2012 at 11:15 PM, Victor Miller <victorsmiller@gmail.com> wrote:
I generalized this problem to the same problem in base b, instead of base 10. I wrote a backtracking program to calculate the number of such sequences for base b=2 through 13. Here are the numbers 2,6,14,20,27,68,41,29,58,20,0,18.
The big surprise is that there were no such sequences in base 12. This sequence isn't in the OEIS. I'll submit it tomorrow.
Victor
On Sun, Mar 4, 2012 at 2:00 AM, Neil Sloane <njasloane@gmail.com> wrote:
Eric, Nice sequence! It is now A208981. It needs more terms, in case anyone wants to help. Neil
On Mon, Jan 2, 2012 at 6:48 PM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
5420976318, 5630187924, 9071532486, etc. In those numbers K, all products of touching digits are visible in K itself (as a substring). For the first K, for instance, the product 5x4 ("20") is a substring of K, as are 4x2 ("8"), 2x0 ("0"), 0x9 ("0"), 9x7 ("63"), 7x6 ("42"), 6x3 ("18"), 3x1 ("3") and 1x8 ("8"). Will you find all such integers -- or at least the smallest and the biggest ones? K integers MUST be 10-digit long and those ten digits must be different one from another. Hope this is not old hat... Best, and HNY to everyone! É.
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