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A102855
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Minimal number of distinct nonzero tetrahedral numbers needed to represent n, or -1 if no such representation is possible.
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6
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1, -1, -1, 1, 2, -1, -1, -1, -1, 1, 2, -1, -1, 2, 3, -1, -1, -1, -1, 1, 2, -1, -1, 2, 3, -1, -1, -1, -1, 2, 3, -1, -1, 3, 1, 2, -1, -1, 2, 3, -1, -1, -1, -1, 2, 3, -1, -1, 3, 4, -1, -1, -1, -1, 2, 1, 2, -1, 3, 2, 3, -1, -1, -1, 3, 2, 3, -1, 4, 3, 4, -1, -1, -1, -1, 2, 3, -1, -1
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OFFSET
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1,5
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LINKS
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MAPLE
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N:= 100; # for a(1)..a(N)
ft:= t -> t*(t+1)*(t+2)/6:
tets:= map(ft, [$1..floor((6*N)^(1/3))]:
f:= proc(n, tmax) option remember;
local res, s;
if member(n, tets) and n < tmax then return 1 fi;
min(seq(1 + procname(n-s, s), s=select(`<`, tets, min(n, tmax))));
end proc:
subs(infinity=-1, map(f, [$1..N], infinity)); # Robert Israel, Dec 29 2019
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MATHEMATICA
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M = 100; (* number of terms *)
ft[t_] := t(t+1)(t+2)/6;
tets = ft /@ Range[1, Floor[(6M)^(1/3)]];
f[n_, tmax_] := f[n, tmax] = If[MemberQ[tets, n] && n < tmax, 1, Min[ Table[1 + f[n-s, s], {s, Select[tets, # < Min[n, tmax]&]}]]];
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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