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

Author

Zhi-Wei Sun, Jul 18 2016

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

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}]