A275169 Positive integers not in the form x^3 + 2*y^2 + z^2 with x,y,z nonnegative integers.

15, 21, 47, 53, 79, 85, 92, 111, 117, 120, 181, 183, 245, 309, 311, 335, 372, 373, 398, 405, 421, 437, 447, 501, 565, 573, 629, 636, 645, 655, 693, 757, 791, 807, 820, 821, 853, 869, 885, 888, 949, 967, 1013, 1045, 1077, 1141, 1205, 1223, 1269, 1271, 1303, 1461, 1555, 1591, 1613, 1653, 2087, 2101, 2255, 2421

Offset

1,1

Comments

Conjecture: The sequence has totally 174 terms as listed in the b-file the largest of which is 375565.

This implies the conjecture in A275150. We note that the sequence contains no term greater than 375565 and not exceeding 10^6.

See also A275168 for a similar conjecture.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..174

Example

a(1) = 15 since 15 is the least positive integer not in the form x^3 + 2*y^2 + z^2 with x,y,z nonnegative integers.

Mathematica

SQ[n_]:=SQ[n]=IntegerQ[Sqrt[n]]
n=0; Do[Do[If[SQ[m-x^3-2*y^2], Goto[aa]], {x, 0, m^(1/3)}, {y, 0, Sqrt[(m-x^3)/2]}]; n=n+1; Print[n, " ", m]; Label[aa]; Continue, {m, 1, 2421}]

Crossrefs

Cf. A000290, A000578, A022551, A022552, A262813, A270488, A274274, A275083, A275150, A275168.

Sequence in context: A334117 A129752 A015831 * A063176 A083372 A119101

Adjacent sequences: A275166 A275167 A275168 * A275170 A275171 A275172

Keyword

nonn

Author

Zhi-Wei Sun, Jul 18 2016

Status

approved