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A087061 Array T(n,k) = lunar sum n+k (n >= 0, k >= 0) read by antidiagonals. 38
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.

We have changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing. - N. J. A. Sloane, Aug 06 2014

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10010

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

D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic, arXiv:1107.1130 [math.NT], 2011.

Index entries for sequences related to dismal (or lunar) arithmetic

EXAMPLE

Lunar addition table begins:

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

   1  1  2  3  4  5  6  7  8  9 11 11 12 13 ...

   2  2  2  3  4  5  6  7  8  9 12 12 12 13 ...

   3  3  3  3  4  5  6  7  8  9 13 13 13 13 ...

   4  4  4  4  4  5  6  7  8  9 14 14 14 14 ...

   5  5  5  5  5  5  6  7  8  9 15 15 15 15 ...

   6  6  6  6  6  6  6  7  8  9 16 16 16 16 ...

   7  7  7  7  7  7  7  7  8  9 17 17 17 17 ...

   8  8  8  8  8  8  8  8  8  9 18 18 18 18 ...

   9  9  9  9  9  9  9  9  9  9 19 19 19 19 ...

  10 11 12 13 14 15 16 17 18 19 10 11 12 13 ...

  11 11 12 13 14 15 16 17 18 19 11 11 12 13 ...

    ...

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 *)

PROG

(PARI) A087061(m, n)={n=Vecrev(digits(if(m<n, m+0*m=n, n))); sum(i=1, #m=Vecrev(digits(m)), if(i>#n, m[i], max(m[i], n[i]))*10^i)\10} \\ M. F. Hasler, Nov 12 2017

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

EXTENSIONS

Edited by M. F. Hasler, Nov 12 2017

STATUS

approved

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Last modified January 18 18:56 EST 2018. Contains 297864 sequences.