OFFSET
1,2
COMMENTS
This sequence gives Theorem 2.2. of Kaplansky, p. 88, with a proof on p. 90.
This sequence is composed of two finite ones and an infinite one: (i) 2*A337217 = {2, 6, 10, 14, 22, 30, 42, 46, 58, 70, 78, 142, 190}, the even members of A094739, (ii) {1, 5, 13, 21, 37, 93, 133, 253}, the 1 (mod 4) members of A094739, and (iii) A002001(k+1) = 4^k*3, for integer k >= 0. Beginning with a(26) = 768 only the powers 4^k*3, for k >= 4 appear.
See eq. (2.2), (2,4), p. 87, of Kaplansky for the two finite sequences with 13 and 8 members, respectively.
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.
FORMULA
See the comment for the union of the three sequences (i), (ii) and (iii).
EXAMPLE
4 is not a member because (x, y, z) = (0, 1, 1) and (2, 0, 0) give both 4.
3 is a member with one solution (1, 0, 1).
5 is a member with one solutuion (1, 1, 1).
7 is not a member because there is no solution.
11 is not a member because there are two solutions (1, 1, 2) and (3, 0, 1).
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Aug 20 2020
STATUS
approved