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

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, 44, 47, 48, 51, 52, 53, 54, 58, 62, 63, 64, 68, 72, 73, 74, 75, 78, 79, 82, 83, 93, 97, 100, 103, 107, 110, 113, 117, 127, 128, 132, 136, 137, 138, 142, 146, 147, 148

Offset: 1

Author

Jud McCranie, Feb 26 2005

Keywords

• nonn
• fini
• full

Comments

The b-file contains all the members of the sequence. See link. - Robert Israel, Dec 29 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..112
• Robert Israel, Proof that the b-file is full

Crossrefs

Cf. A000292, A104246, A102795, etc.

Programs

Maple

N:= 100000: # to test all n <= 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 false fi;
   for s in tets while s < min(n, tmax) do
     if not procname(n-s,s) then return false fi
   od;
     true
end proc:
select(f, [$1..N],infinity); # Robert Israel, Dec 29 2019

Mathematica

M = 1000; (* to test all n <= M *)
ft[t_] := t*(t+1)*(t+2)/6;
tets = Map[ft, Range[Floor[(6*M)^(1/3)]]];
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];
Select[Range[M], f[#, Infinity]&] (* Jean-François Alcover, Sep 15 2022, after Robert Israel *)