A394229 a(n) is the first start of exactly n consecutive numbers that are not the sum of a nonnegative cube and a triangular number.

5, 12, 24, 38, 94, 57, 505, 390, 262, 872, 451, 480, 604, 2114, 1569, 2056, 1258, 1962, 7218, 13008, 1303, 9670, 6512, 7695, 14618, 6401, 6585, 35868, 13779, 22548, 57097, 31970, 53238, 17482, 27631, 21764, 40433, 103009, 47833, 29579, 87083, 49367, 73401, 118731, 120214, 222462, 224045, 144042

Offset

1,1

Comments

a(n) is the start of a run of exactly n consecutive numbers in A014156.

Links

Table of n, a(n) for n=1..48.

Example

a(3) = 24 because 24, 25 and 26 are not the sum of a nonnegative cube and a triangular number, but 23 = 2^3 + 5*6/2 and 27 = 3^3 + 0*1/2 are.

Maple

N:= 10^7: # for terms before the first term > N
nC:= floor(surd(N, 3)): C:= {seq(i^3, i=0..nC)}:
nT:= floor((sqrt(1+8*N)-1)/2): T:= {seq(i*(i+1)/2, i=0..nT)}:
A:= sort(convert(select(`<=`, {seq(seq(c+t, c=C), t=T)}, N), list)):
dA:= A[2..-1]-A[1..-2]:
m:= min({$1..max(dA)+1} minus convert(dA, set)):
V:= Vector(m-2);
for i from 2 to m-1 do
if member(i, dA, 'k') then V[i-1]:= A[k]+1 fi
od;
convert(V, list);

Crossrefs

Cf. A014156.

Sequence in context: A100479 A018806 A101425 * A191831 A365540 A384562

Adjacent sequences: A394226 A394227 A394228 * A394230 A394231 A394232

Keyword

nonn

Author

Robert Israel, Apr 17 2026

Status

approved