login
A275169
Positive integers not in the form x^3 + 2*y^2 + z^2 with x,y,z nonnegative integers.
4
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
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}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Jul 18 2016
STATUS
approved