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Journal of Integer Sequences, Vol. 14 (2011), Article 11.9.8

Dismal Arithmetic


David Applegate
AT&T Shannon Labs
180 Park Avenue
Florham Park, NJ 07932-0971
USA

Marc LeBrun
Fixpoint Inc.
448 Ignacio Blvd., #239
Novato, CA 94949
USA

N. J. A. Sloane
AT&T Shannon Labs
180 Park Avenue
Florham Park, NJ 07932-0971
USA

Abstract:

Dismal arithmetic is just like the arithmetic you learned in school, only simpler: there are no carries, when you add digits you just take the largest, and when you multiply digits you take the smallest. This paper studies basic number theory in this world, including analogues of the primes, number of divisors, sum of divisors, and the partition function.

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(Concerned with sequences A000045 A000695 A000931 A002378 A003465 A006498 A007059 A009994 A009996 A027444 A048888 A054244 A067139 A067398 A067399 A070550 A079500 A079968 A079976 A087019 A087029 A087052 A087079 A087097 A087416 A087636 A087984 A088469 A088470 A088471 A088472 A088473 A088475 A088476 A088477 A088478 A088479 A088480 A088481 A144171 A144175 A156041 A161813 A162672 A164387 A169912 A171000 A171004 A171120 A171786 A171787 A171788 A171789 A171794 A171795 A171796 A171818 A172199 A180513 A181319 A184957 A186413 A186442 A186443 A186523 A186636 A188223 A188288 A188548 A189101 A189506 A189788 A190149 A190150 A190151 A190632 A190820 A191420 A191674 A191675 A191701 A191752 A191753)

Received July 7 2011; revised version received October 25 2011. Published in Journal of Integer Sequences, November 21 2011.

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