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A102806 Numbers that are not the sum of distinct tetrahedral numbers.

%I A102806 #17 Sep 15 2022 10:38:37
%S A102806 2,3,6,7,8,9,12,13,16,17,18,19,22,23,26,27,28,29,32,33,37,38,41,42,43,
%T A102806 44,47,48,51,52,53,54,58,62,63,64,68,72,73,74,75,78,79,82,83,93,97,
%U A102806 100,103,107,110,113,117,127,128,132,136,137,138,142,146,147,148
%N A102806 Numbers that are not the sum of distinct tetrahedral numbers.
%C A102806 The b-file contains all the members of the sequence.  See link. - _Robert Israel_, Dec 29 2019
%H A102806 Robert Israel, <a href="/A102806/b102806.txt">Table of n, a(n) for n = 1..112</a>
%H A102806 Robert Israel, <a href="/A102806/a102806.pdf">Proof that the b-file is full</a>
%p A102806 N:= 100000: # to test all n <= N
%p A102806 ft:= t -> t*(t+1)*(t+2)/6:
%p A102806 tets:= map(ft, [$1..floor((6*N)^(1/3))]):
%p A102806 f:= proc(n,tmax) option remember;
%p A102806    local res, s;
%p A102806    if member(n, tets) and n < tmax then return false fi;
%p A102806    for s in tets while s < min(n, tmax) do
%p A102806      if not procname(n-s,s) then return false fi
%p A102806    od;
%p A102806      true
%p A102806 end proc:
%p A102806 select(f, [$1..N],infinity); # _Robert Israel_, Dec 29 2019
%t A102806 M = 1000; (* to test all n <= M *)
%t A102806 ft[t_] := t*(t+1)*(t+2)/6;
%t A102806 tets = Map[ft, Range[Floor[(6*M)^(1/3)]]];
%t A102806 f[n_, tMax_] := f[n, tMax] = Module[{res, s}, If[MemberQ[tets, n] && n < tMax, Return[False]]; For[i = 1, s = tets[[i]]; i <= Length[tets] && s < Min[n, tMax], i++, If[!f[n-s, s], Return[False]]]; True];
%t A102806 Select[Range[M], f[#, Infinity]&] (* _Jean-François Alcover_, Sep 15 2022, after _Robert Israel_ *)
%Y A102806 Cf. A000292, A104246, A102795, etc.
%K A102806 nonn,fini,full
%O A102806 1,1
%A A102806 _Jud McCranie_, Feb 26 2005