0,4

There are no carries in dismal arithmetic. For each pair of dismal digits, to Add, take the lArger, but to Multiply, take the sMaller. For example:

.....169

...+.248

...------

.....269

and

.......169

.....x.248

.....------

.......168

......144

...+.122

...--------

.....12468

Addition and multiplication are associative and commutative, and multiplication distributes over addition. E.g. 357 * (169 + 248) = 357 * 269 = 23567 = 13567 + 23457 = (357 * 169) + (357 * 248). Note that 0+x = x and 9*x = x for all x.

D. Applegate, C program for dismal arithmetic and number theory

Index entries for sequences related to dismal arithmetic

Dismal addition table begins:

0 1 2 3 4 5 ...

1 1 2 3 4 5 ...

2 2 2 3 4 5 ...

3 3 3 3 4 5 ...

...

Maple programs for dismal arithmetic are in A087062.

Cf. A087062 (multiplication).

Adjacent sequences: A087058 A087059 A087060 this_sequence A087062 A087063 A087064

Sequence in context: A049819 A079056 A003984 this_sequence A082860 A098357 A058071

nonn,tabl,nice,base

Marc LeBrun (mlb(AT)well.com), Oct 09 2003