

A087061


Array T(n,k) = lunar sum n+k (n >= 0, k >= 0) read by antidiagonals.


37



0, 1, 1, 2, 1, 2, 3, 2, 2, 3, 4, 3, 2, 3, 4, 5, 4, 3, 3, 4, 5, 6, 5, 4, 3, 4, 5, 6, 7, 6, 5, 4, 4, 5, 6, 7, 8, 7, 6, 5, 4, 5, 6, 7, 8, 9, 8, 7, 6, 5, 5, 6, 7, 8, 9, 10, 9, 8, 7, 6, 5, 6, 7, 8, 9, 10, 11, 11, 9, 8, 7, 6, 6, 7, 8, 9, 11, 11, 12, 11, 12, 9, 8, 7, 6, 7, 8, 9, 12, 11, 12, 13, 12, 12, 13, 9, 8
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OFFSET

0,4


COMMENTS

There are no carries in lunar arithmetic. For each pair of lunar 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.


LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10010
D. Applegate, C program for lunar arithmetic and number theory [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic"  the old name was too depressing]
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011. [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic"  the old name was too depressing]
Index entries for sequences related to dismal (or lunar) arithmetic


EXAMPLE

Lunar 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

Maple programs for lunar arithmetic are in A087062.


MATHEMATICA

ladd[x_, y_] := FromDigits[MapThread[Max, IntegerDigits[#, 10, Max @@ IntegerLength /@ {x, y}] & /@ {x, y}]]; Flatten[Table[ladd[k, n  k], {n, 0, 13}, {k, 0, n}]] (* Davin Park, Sep 29 2016 *)


CROSSREFS

Cf. A087062 (multiplication), A087097 (primes).
Sequence in context: A079056 A231205 A003984 * A082860 A283845 A058071
Adjacent sequences: A087058 A087059 A087060 * A087062 A087063 A087064


KEYWORD

nonn,tabl,nice,base,look


AUTHOR

Marc LeBrun, Oct 09 2003


STATUS

approved



