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

1,1

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

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 *)

Crossrefs

Cf. A000292, A104246, A102795, etc.

Sequence in context: A037460 A285134 A161824 * A275884 A003605 A344128

Adjacent sequences: A102803 A102804 A102805 * A102807 A102808 A102809

Keyword

nonn,fini,full

Author

Jud McCranie, Feb 26 2005

Status

approved