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A135558
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Sums of three distinct nonzero Fibonacci numbers.
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3
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6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 52, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 68, 69, 70, 71, 73, 76, 77, 78, 79, 81, 84, 89, 90, 91, 92, 93, 94, 95
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OFFSET
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1,1
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COMMENTS
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These numbers may have more than one such representation.
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LINKS
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MAPLE
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isA135558 := proc(n) # returns true if n is in the sequence
local xi, yi, x, y, z ;
for xi from 2 do
if 3*x > n then
return false;
end if;
for yi from xi+1 do
if x+2*y > n then
break;
else
z := n-x-y ;
if z >y and isA000045(z) then # see isFib in A000045
return true;
end if;
end if;
end do:
end do:
end proc:
option remember;
local a;
if n = 1 then
6;
else
for a from procname(n-1)+1 do
if isA135558(a) then
return a;
end if;
end do:
end if;
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MATHEMATICA
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fibs[n_ /; n >= 6] := Reap[Module[{k = 1}, While[Fibonacci[k] < n, Sow[Fibonacci[k++]]]]][[2, 1]];
okQ[n_] := AnyTrue[IntegerPartitions[n, {3}, fibs[n]], Length[Union[#]] == 3&];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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