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Only 9 (which has an unhelpful cube-Ï‰ relation to the base) and B (dozenal E, decimal 11) are opaque in ununimal. 2, 3, 4 and 6 benefit from the proximity to dozen, getting them the digit-sum test; 7 gets the alternating digit sum difference test from the neighbour upstairs; 5 uses SPD as in dozenal; and 8, like the one additional binary power in all odd bases, is a square-Ï‰ inheritor and can therefore be tested for after compacting the tested number down to two digits by summing up pairs of digits.Oschkar wrote:In fact, tridecimal has memorable tests for the first seven primes except 11.
Both are subjective terms. I only objected to 'intuitive' because it implies a elementary schooler can discover the test all on his own, which I think holds true only for the divisor, semidivisor and placeholder* tests. Even the digit-sum wouldn't occur to a young child except as a fluke.icarus wrote:Again the designation â€œintuitiveâ€ is a construction; in the new work weâ€™ll go beyond intuitive, to â€œpracticalâ€.
SPD is an involved test; perhaps easy enough once you get the required multiples memorised, but it still hasn't got the same out-of-hand usability to it as the digit-sum and alternating-digits tests. The only thing that makes it worthy of note is that, finally, finally, after a long time trying to get the prime 5 into the dozenal fold in various ways, we've got a complete test for 5 in dozenal. I might say SPD is remarkable in a 'world's tallest midget' kind of way.I think techniques like SPD and the higher mod-1 tests wonâ€™t be â€œfirst-tierâ€ considerations but do need to be discussed when we delve into the divisibility test portion of any base.
Lucky you. I usually doodle in bases 14 and 22, and sometimes 70.I was looking for properties of base 18 and then for the rest of the day I found myself thinking in octodecimal completely.
I'm for such range folding as a scaffold, to be used until you've memorised the table straight out. There must, however, be some upper limit beyond which the scaffold becomes permanent. I think I could memorise the basic multiplication table row of 5 in base *28 (2â†‘5), but never the entire extended block of a bit over two hundred 2-digit multiples.icarus wrote:in effect all we need is what we would have learned in 2nd grade: the multiples of 5 in the multiplication table, then recognizing that the pattern repeats every five dozen. With this we can construct the required range until it stands on its own.
I was about to write a suitably Icarian overview of bases 17, 19, 34, 55, 64, 99 and 2520, thinking that you wouldnâ€™t return to the Forum. At least Iâ€™m glad to see that youâ€™re back. Also, my Argam Kinsevoctove extension is done.icarus @ Jun 19 2013, 12:18 PM wrote: Folks we are coming out of the darkness. Have had to do some business development, then have had a surge of work that commanded all my time. Still about a week from when I can return. There is a lot to read in the forum.
Hope all are well.