cp's OEIS Frontend

A102855 Minimal number of distinct nonzero tetrahedral numbers needed to represent n, or -1 if no such representation is possible.

%I A102855 #11 Aug 05 2022 07:42:42
%S A102855 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,
%T A102855 -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,
%U A102855 -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
%N A102855 Minimal number of distinct nonzero tetrahedral numbers needed to represent n, or -1 if no such representation is possible.
%H A102855 Robert Israel, <a href="/A102855/b102855.txt">Table of n, a(n) for n = 1..10000</a>
%p A102855 N:= 100; # for a(1)..a(N)
%p A102855 ft:= t -> t*(t+1)*(t+2)/6:
%p A102855 tets:= map(ft, [$1..floor((6*N)^(1/3))]:
%p A102855 f:= proc(n,tmax) option remember;
%p A102855    local res, s;
%p A102855    if member(n, tets) and n < tmax then return 1 fi;
%p A102855    min(seq(1 + procname(n-s,s), s=select(`<`,tets,min(n,tmax))));
%p A102855 end proc:
%p A102855 subs(infinity=-1,map(f, [$1..N],infinity)); # _Robert Israel_, Dec 29 2019
%t A102855 M = 100; (* number of terms *)
%t A102855 ft[t_] := t(t+1)(t+2)/6;
%t A102855 tets = ft /@ Range[1, Floor[(6M)^(1/3)]];
%t A102855 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]&]}]]];
%t A102855 f[#, Infinity]& /@ Range[1, M] /. Infinity -> -1 (* _Jean-François Alcover_, Aug 05 2022, after _Robert Israel_ *)
%Y A102855 Cf. A104246, A102795-A102806, A102856-A102858.
%K A102855 sign
%O A102855 1,5
%A A102855 _Jud McCranie_, Mar 01 2005