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

%I

%S 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,

%T 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,

%U 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

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

%C 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:

%C 169

%C + 248

%C ------

%C 269

%C and

%C 169

%C x 248

%C ------

%C 168

%C 144

%C + 122

%C --------

%C 12468

%C 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.

%C We have changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing. - _N. J. A. Sloane_, Aug 06 2014

%H Alois P. Heinz, <a href="/A087061/b087061.txt">Table of n, a(n) for n = 0..10010</a>

%H D. Applegate, <a href="/A087061/a087061.txt">C program for lunar arithmetic and number theory</a>

%H D. Applegate, M. LeBrun and N. J. A. Sloane, <a href="http://arxiv.org/abs/1107.1130">Dismal Arithmetic</a>, arXiv:1107.1130 [math.NT], 2011.

%H Brady Haran and N. J. A. Sloane, <a href="https://youtu.be/cZkGeR9CWbk">Primes on the Moon (Lunar Arithmetic)</a>, Numberphile video, Nov 2018.

%H <a href="/index/Di#dismal">Index entries for sequences related to dismal (or lunar) arithmetic</a>

%e Lunar addition table begins:

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

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

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

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

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

%e 5 5 5 5 5 5 6 7 8 9 15 15 15 15 ...

%e 6 6 6 6 6 6 6 7 8 9 16 16 16 16 ...

%e 7 7 7 7 7 7 7 7 8 9 17 17 17 17 ...

%e 8 8 8 8 8 8 8 8 8 9 18 18 18 18 ...

%e 9 9 9 9 9 9 9 9 9 9 19 19 19 19 ...

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

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

%e ...

%p Maple programs for lunar arithmetic are in A087062.

%t 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 *)

%o (PARI) ladd=A087061(m,n)=fromdigits(vector(if(#(m=digits(m))>#n=digits(n),#n=Vec(n,-#m),#m<#n,#m=Vec(m,-#n),#n),k,max(m[k],n[k]))) \\ _M. F. Hasler_, Nov 12 2017, updated Nov 15, 2018

%Y Cf. A087062 (multiplication), A087097 (primes).

%K nonn,tabl,nice,base,look

%O 0,4

%A _Marc LeBrun_, Oct 09 2003

%E Edited by _M. F. Hasler_, Nov 12 2017

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Last modified August 17 11:14 EDT 2019. Contains 326057 sequences. (Running on oeis4.)