A093519 Numbers with no representation as the sum of two (not necessarily distinct) generalized pentagonal numbers.

11, 18, 21, 25, 32, 39, 43, 46, 49, 54, 60, 65, 67, 68, 74, 76, 81, 87, 88, 90, 95, 98, 106, 109, 111, 113, 116, 120, 123, 125, 130, 136, 137, 142, 144, 153, 158, 159, 163, 164, 165, 172, 173, 175, 179, 182, 186, 193, 197, 201, 204, 205, 207, 208, 214, 219, 220

Offset: 1

Author

Jon Perry, Mar 29 2004

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001318 (generalized pentagonal numbers), A093518.

Cf. A204382.

Programs

Maple

GP:= [0, seq(op([m*(3*m-1)/2, m*(3*m+1)/2]), m=1..50)]:
N:= GP[-1]:
V:= Array(0..N, datatype=integer[4]):
for i from 1 to nops(GP) do
for j from 1 to i do
   r:= GP[i]+GP[j];
   if r > N then break fi;
   V[r]:= V[r]+1
od od:
select(t -> V[t] = 0, [$0..N]); # Robert Israel, Feb 26 2025

Extensions

Definition clarified by Robert Israel, Feb 26 2025