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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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified June 24 15:07 EDT 2017. Contains 288697 sequences.