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A280635
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Numbers whose digit string can be partitioned into three nonempty parts such that the product of the first two parts equals the third part.
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4
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111, 122, 133, 144, 155, 166, 177, 188, 199, 212, 224, 236, 248, 313, 326, 339, 414, 428, 515, 616, 717, 818, 919, 2510, 2612, 2714, 2816, 2918, 3412, 3515, 3618, 3721, 3824, 3927, 4312, 4416, 4520, 4624, 4728, 4832, 4936, 5210, 5315, 5420, 5525, 5630, 5735
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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Could be called "area numbers" since if the first set of digits is the length, and the second set of digits is the width, then the last set of digits is the area, with length * width = area.
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LINKS
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EXAMPLE
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236 is in the sequence since 2*3=6. 3515 is in the sequence since 3*5=15. Leading zeros are not allowed, thus 2036 (2*03=6) is not included.
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MAPLE
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read("transforms") : # implements digcatL
isA280635 := proc(n)
local dgs, spl1, spl2, dgs1, dgs2, dgs3;
dgs := convert(n, base, 10) ;
if nops(dgs) >= 3 then
for spl1 from 1 to nops(dgs)-2 do
for spl2 from spl1+1 to nops(dgs)-1 do
if op(-1, dgs) <> 0 and op(spl1, dgs) <> 0 and op(spl2, dgs) <> 0 then
dgs1 := ListTools[Reverse]([op(spl2+1..nops(dgs), dgs)]) ;
dgs2 := ListTools[Reverse]([op(spl1+1..spl2, dgs)]) ;
dgs3 := ListTools[Reverse]([op(1..spl1, dgs)]) ;
if digcatL(dgs1)*digcatL(dgs2) = digcatL(dgs3) then
return true;
end if
end if;
end do:
end do:
false ;
else
false;
end if;
end proc:
for n from 100 do
if isA280635(n) then
printf("%d, \n", n) ;
end if;
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MATHEMATICA
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With[{nn = 1}, Union@ Flatten@ Table[FromDigits@ Flatten@ Map[IntegerDigits, {n, k, n k}], {n, 10^nn - 1}, {k, 10^nn - 1}]] (* Michael De Vlieger, Jan 07 2017 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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