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User: Will Jagy

Will Jagy has authored 2 sequences.

A094682 Discriminants of integer positive ternary quadratic forms that are spinor regular but not regular.

64, 108, 108, 128, 256, 256, 324, 343, 432, 432, 432, 1024, 1024, 1024, 1372, 1728, 2048, 3888, 4096, 4096, 4096, 5488, 6912, 6912, 16384, 16384, 27648, 62208, 87808

Offset: 1

Will Jagy, Jun 03 2004

List is believed to be complete.

G. L. Watson: Integral Quadratic Forms (Cambridge, 1960).

W. K. Chan and A. G. Earnest, Discriminant bounds for spinor regular ternary quadratic lattices, J. London Math. Soc. (2) 69 (2004), no. 3, 545-561.
W. C. Jagy, I. Kaplansky and A. Schiemann, There are 913 regular ternary forms, Mathematika 44(1997) 332-341.
A. Schiemann, Ternary positive definite quadratic forms are determined by their theta series, Math. Ann. 308(1997) 507-517.

A022552 Numbers that are not the sum of 2 squares and a nonnegative cube.

Original entry on oeis.org

7, 15, 22, 23, 39, 55, 70, 71, 78, 87, 94, 103, 111, 115, 119, 120, 139, 167, 211, 254, 263, 267, 279, 286, 302, 311, 312, 331, 335, 342, 391, 403, 435, 454, 455, 470, 475, 499, 518, 559, 590, 595, 598, 622, 643, 659, 691, 695, 715, 727, 771

Offset: 1

N. J. A. Sloane, Will Jagy

nonn

There are 434 terms < 6 * 10^7 of which the largest is 5042631 ~= 5 * 10^6. Is this sequence finite? - David A. Corneth, Jun 23 2018
No more terms < 10^10. - Mauro Fiorentini, Jan 26 2019
For n = 1..434, a(n) + 2 is a term of A022551. Zhi-Wei Sun conjectures that Any n can be written as x^2 + y^2 + z^3 + 0(or 2). - XU Pingya, Jun 02 2020

R. J. Mathar, David A. Corneth, Table of n, a(n) for n = 1..434 (First 325 terms from R. J. Mathar, now terms < 6 * 10^7)
Steven Finch, Pattern-Avoiding Permutations [Broken link?]
Steven Finch, Pattern-Avoiding Permutations [Cached copy, with permission]
W. Jagy and I. Kaplansky, Sums of Squares, Cubes and Higher Powers, Experimental Mathematics, vol. 4 (1995) pp. 169-173.
Zhi-Wei Sun, New Conjectures on Representations of Integers (I), Nanjing Univ. J. Math. Biquarterly 34(2017), No.2, p. 110.
Index entries for sequences related to sums of squares

Complement of A022551.

isA022552 := proc(n)
    not isA022551(n) ;
end proc:
n := 1:
for c from 0 do
    if isA022552(c) then
        printf("%d %d\n",n,c);
        n := n+1 ;
    end if;
end do: # R. J. Mathar, Sep 02 2016

max = 10^6;
Table[x^2 + y^2 + z^3, {x, 0, Sqrt[max]}, {y, x, Sqrt[max - x^2]}, {z, 0, (max - x^2 - y^2)^(1/3)}] // Flatten // Union // Select[#, # <= max&]& // Complement[Range[max], #]& (* Jean-François Alcover, Mar 23 2020 *)

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User: Will Jagy

A094682 Discriminants of integer positive ternary quadratic forms that are spinor regular but not regular.

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A022552 Numbers that are not the sum of 2 squares and a nonnegative cube.

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