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A261684 Array T(n,k) = lunar product n*k (n >= 0, k >= 0) read by antidiagonals. 3
0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 2, 1, 0, 0, 1, 2, 2, 1, 0, 0, 1, 2, 3, 2, 1, 0, 0, 1, 2, 3, 3, 2, 1, 0, 0, 1, 2, 3, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 4, 3, 2, 1, 0, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 0, 0, 10, 2, 3, 4, 5, 5, 4, 3, 2, 10, 0, 0, 11, 10, 3, 4, 5, 6, 5, 4, 3, 10, 11, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

See A087061 for definition. Note that 0+x = x and 9*x = x for all x.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..20099

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 [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]

Brady Haran and N. J. A. Sloane, Primes on the Moon (Lunar Arithmetic), Numberphile video, Nov 2018.

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

EXAMPLE

Lunar multiplication table begins:

0 0 0 0 0 0 ...

0 1 1 1 1 1 ...

0 1 2 2 2 2 ...

0 1 2 3 3 3 ...

0 1 2 3 4 4 ...

0 1 2 3 4 5 ...

....

MAPLE

# convert decimal to string:

rec := proc(n) local t0, t1, e, l; if n <= 0 then RETURN([[0], 1]); fi; t0 := n mod 10; t1 := (n-t0)/10; e := [t0]; l := 1; while t1 <> 0 do t0 := t1 mod 10; t1 := (t1-t0)/10; l := l+1; e := [op(e), t0]; od; RETURN([e, l]); end;

# convert string to decimal:

cer := proc(ep) local i, e, l, t1; e := ep[1]; l := ep[2]; t1 := 0; if l <= 0 then RETURN(t1); fi; for i from 1 to l do t1 := t1+10^(i-1)*e[i]; od; RETURN(t1); end;

# lunar addition:

dadd := proc(m, n) local i, r1, r2, e1, e2, l1, l2, l, l3, t0; r1 := rec(m); r2 := rec(n); e1 := r1[1]; e2 := r2[1]; l1 := r1[2]; l2 := r2[2]; l := max(l1, l2); l3 := min(l1, l2); t0 := array(1..l); for i from 1 to l3 do t0[i] := max(e1[i], e2[i]); od; if l>l3 then for i from l3+1 to l do if l1>l2 then t0[i] := e1[i]; else t0[i] := e2[i]; fi; od; fi; cer([t0, l]); end;

# lunar multiplication:

dmul := proc(m, n) local k, i, j, r1, r2, e1, e2, l1, l2, l, t0; r1 := rec(m); r2 := rec(n); e1 := r1[1]; e2 := r2[1]; l1 := r1[2]; l2 := r2[2]; l := l1+l2-1; t0 := array(1..l); for i from 1 to l do t0[i] := 0; od; for i from 1 to l2 do for j from 1 to l1 do k := min(e2[i], e1[j]); t0[i+j-1] := max(t0[i+j-1], k); od; od; cer([t0, l]); end;

# to produce the b-file:

M:=199; c:=0; for n from 0 to M do for k from 0 to n do lprint(c, dmul(n-k, k)); c:=c+1; od: od:

CROSSREFS

Cf. A087061 (addition).

See A087062 for a version that excludes the zero row and column.

Similar to but different from A003983.

Sequence in context: A324734 A111143 A004197 * A048571 A025880 A058755

Adjacent sequences:  A261681 A261682 A261683 * A261685 A261686 A261687

KEYWORD

nonn,tabl,look,hear

AUTHOR

N. J. A. Sloane, Sep 06 2015

STATUS

approved

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Last modified May 25 08:37 EDT 2020. Contains 334587 sequences. (Running on oeis4.)