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A087062
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Array T(n,k) = dismal product n*k (n >= 1, k >= 1) read by antidiagonals.
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18
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1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 3, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 3, 4, 3, 2, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 2, 3, 4, 5, 4, 3, 2, 1, 10, 2, 3, 4, 5, 5, 4, 3, 2, 10, 11, 10, 3, 4, 5, 6, 5, 4, 3, 10, 11, 11, 11, 10, 4, 5, 6, 6, 5, 4, 10, 11, 11, 11, 12, 11, 10, 5, 6, 7, 6, 5, 10, 11, 12, 11, 11, 12, 12
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| See A087061 for definition. Note that 0+x = x and 9*x = x for all x.
This differs from A003983 at a(46): min(1,10)=1, while dismal product 10*1 = 10.
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LINKS
| Alois P. Heinz, Table of n, a(n) for n = 1..10011
D. Applegate, C program for dismal arithmetic and number theory
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic
Index entries for sequences related to dismal arithmetic
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EXAMPLE
| Dismal multiplication table begins:
1 1 1 1 1 ...
1 2 2 2 2 ...
1 2 3 3 3 ...
1 2 3 4 4 ...
1 2 3 4 5 ...
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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;
# dismal 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;
# dismal 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;
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CROSSREFS
| Cf. A087061 (addition).
Sequence in context: A054526 A113453 A003983 * A204026 A110537 A144434
Adjacent sequences: A087059 A087060 A087061 * A087063 A087064 A087065
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KEYWORD
| nonn,tabl,nice,base
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AUTHOR
| Marc LeBrun (mlb(AT)well.com), Oct 09 2003
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EXTENSIONS
| Maple programs from N. J. A. Sloane (njas(AT)research.att.com).
Incorrect comment and Mathematica program removed by David Applegate (david(AT)research.att.com), Jan 03 2012
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