============================================================ THE DSA NEWSCAST http://www.dozenal.org ============================================================ The Dozenal Society of America Vol. 2, Iss. 7 Official Newsletter 3 July 11EX ============================================================ ============================================================ = CONTENTS = ============================================================ 1. Donations 2. For Sale 3. Dozenal News 4. Society Business 5. Poetical Diversion 6. Backmatter ============================================================ = DONATIONS = ============================================================ Members, please remember that while dues are no longer required for membership, we still rely on the generosity of members to keep the DSA going. Donations of any amount, large or small, are welcome and needed. A donation of $10; ($12.) will procure Subscription membership, and entitles the payer to receive both a digital and a paper copy of the _Bulletin_ if requested. Other members will receive only a digital copy. To invoke this privilege, please notify the Editor of the Bulletin, Mike deVlieger, at mdevlieger@dozenal.org As members know, we are a volunteer organization which pays no salaries. As such, every penny you donate goes toward furthering the DSA's goals. It may be worth considering a monthly donation; say, $3, or $6, or whatever seems reasonable to you. This can be set up quite easily with Paypal or WePay, both of which are available at our web site. Of course, if you prefer to donate by check, you may send them to our worthy Treasurer, Jay Schiffman, payable to the Dozenal Society of America, at: Jay Schiffman 604-36 South Washington Square, #815 Philadelphia, PA 19106-4115 ----------------------Member Benefits----------------------- Chief among the benefits of membership, aside from the knowledge of supporting the DSA's mission, is receipt of _The Duodecimal Bulletin_. In addition, however, members also receive (digitally) a membership card containing their vital member information and a monthly calendar with dozenal numbers, containing suitable and educational dozenal quotations and graphics, laid out for wall display. To receive these, please notify us that you'd like to receive them: Contact@dozenal.org ============================================================ = FOR SALE = ============================================================ The DSA is pleased to offer the following for sale. These are all either at cost, or the proceeds go to the Society. Wall Calendar for 11EX (stapled binding) $11.60 Wall Calendar for 11EX, coiled binding $16.70 Weekly Planner for 11EX $11.29 TGM: A Coherent Dozenal Metrology $8.00 Prices are, unfortunately but by necessity, in decimal. To find these works, simply go to: http://www.lulu.com/shop/shop.ep and enter the appropriate terms. E.g., searching for "11EX" will turn up these calendars and the planner; searching for "TGM dozenal" will turn up the TGM book. We hope to offer other titles, and even some other items (such as dozenal clocks and the like), in the near future. ============================================================ = DOZENAL NEWS = ============================================================ Our esteemed editor, Michael De Vlieger (#37E), has submitted three new sequences to the Online Encyclopedia of Integer Sequences (OEIS), and greatly extended another. The following is Mike's own words on these contributions. Two new OEIS sequences associated with the neutral digits m of base n. A neutral digit m < n neither divides n nor is coprime to n. These are counted by a pre-existing sequence A045763, which Mike has extended to 10,000 values from 1000. Sequence A243822 lists the smallest 10,000 values of the semidivisor counting function. A semidivisor is a regular digit m < n that does not divide base n. A regular digit (counted by pre-existing A010846) is one, all of whose prime divisors p also divide the base n. Dozenal {8, 9} are semidivisors, while {1, 2, 3, 4, 6, 8, 9, 10;} are dozenal regular. Thus A010846 - A000005 (the divisor counting function) = A243822. Sequence A243823 lists the smallest 10,000 values of the semitotative counting function. A semitotative is a product of at least one prime divisor p of n and one prime q coprime to n. Thus A045763 = A243822 + A243823. Dozenal digit ten is a semitotative; in base ten, 6 is semitotative. During the consideration of these neutral digit functions, Mike has extended the sequences A010846 and A105110. The sequences were generated by Mathematica scripts. The two types of neutral digit derive from a 2011 proof Mike wrote. There are four digit types, divisor, totative, semidivisor, and semitotative; with these it is possible to understand a number base more clearly, simply by the behavior of its digits. Further sequences under review have to do with regular digits. These regular digits m of base n have unit fractions that terminate in base n. An example is decimal 4 or dozenal 9: decimal 1/4 = .25 and dozenal 1/9 is .14. Proposed sequence A244052 lists bases m which set a record number of regular digits. (It is the record transform of A010846). The function is similar to the highly composite numbers A002182. These bases have more regular digits (whose unit fractions have a terminating expansion in that base) than the previous base: {2, 4, 6, 10, 12, 18, 24, 30, 42, 60, ...}. Mike has generated 53 terms (up to base 53130) at the time of writing. Finally, the values associated with these bases constitute proposed sequence A244053. http://www.oeis.org/A243822 http://www.oeis.org/A243823 http://www.oeis.org/A244053 Thanks, Mike, for sharing this. ============================================================ = SOCIETY BUSINESS = ============================================================ Unfortunately, we've still received no more definite information for when in the Richmond conference the DSA's program will be set, so we're unable to give more definite information about the date and time of our annual conference. We will share more details as soon as they become available. ============================================================ = POETICAL DIVERSION = ============================================================ Why hot dogs buns still come in tens, but hot dogs come in only eight will ever be a mystery to me; And why does sausage come in fives, and cats possess a full nine lives, but golf balls come in tins of only three? And why's a sibling one degree, A parent's sibling's son full three, but mother's sister's daughter's still my cousin? So many numbers! But don't fret; If we need more, then more we'll get; But everything's still cheaper by the dozen! ============================================================ = BACKMATTER = ============================================================ _The DSA Newscast_ is a production of the Dozenal Society of America. If you have received this publication in error, or otherwise do not wish to receive it anymore, please unsubscribe by mailing a message containing the string "UNSUBSCRIBE NEWSCAST", exactly as typed, in its body, to the Reply-To address of this message. For questions, comments, submissions, or other communication with the _Newscast_, please write to: newscast@dozenal.org EACH ONE, TEACH ONE