Dismal arithmetic. (English) Zbl 1290.11007
Summary: 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.
MSC:
11A63 | Radix representation; digital problems |
06A06 | Partial orders, general |
11A25 | Arithmetic functions; related numbers; inversion formulas |
Keywords:
carryless arithmetic; squares; primes; divisors; compositions; partitions; asymptotic expansions; Mellin transformOnline Encyclopedia of Integer Sequences:
Padovan sequence (or Padovan numbers): a(n) = a(n-2) + a(n-3) with a(0) = 1, a(1) = a(2) = 0.Numbers with digits in nondecreasing order.