A337217 One half of the even numbers of A094739.

1, 3, 5, 7, 11, 15, 21, 23, 29, 35, 39, 71, 95

Offset

1,2

Comments

This finite sequence a(n), for n = 1, 2, ..., 13, appears as eq. (2.3) given by Kaplansky on p. 87.

It enters Theorem 2.1 of Kaplansky, p. 87, with proof on p. 90 (here reformulated): The positive integers uniquely represented by x^2 + y^2 + 2*z^2, with 0 <= x <= y and 0 <= z, consist of the 13 numbers a(n) and 4^k*6 = A002023(k), for integers k >= 0. See a comment in A002023 for this uniquely representable positive integers of this ternary form.

It also enters Theorem 2.3 of Kaplansky, p. 88, with proof on p.91 (here reformulated): The positive integers uniquely represented by x^2 + 2*y^2 + 4*z^2, with nonnegative integers x, y, z consist of the 13 odd numbers a(n) and the four even numbers 2, 10, 26, and 74. This is the finite sequence

1, 2, 3, 5, 7, 10, 11, 15, 21, 23, 26, 29, 35, 39, 71, 74, 95.

References

Irving Kaplansky, Integers Uniquely Represented by Certain Ternary Forms, in "The Mathematics of Paul Erdős I", Ronald. L. Graham and Jaroslav Nešetřil (Eds.), Springer, 1997, pp. 86 - 94.

Links

Table of n, a(n) for n=1..13.

Crossrefs

Cf. A002023, A094739, A337218.

Sequence in context: A007665 A208994 A194602 * A333380 A361826 A177139

Adjacent sequences: A337214 A337215 A337216 * A337218 A337219 A337220

Keyword

nonn,fini,full

Author

Wolfdieter Lang, Aug 20 2020

Status

approved