

A306929


Numbers k (>0) such that x^2+y^2 and x^2+k*y^2 can be simultaneously squares.


2



1, 7, 10, 11, 17, 20, 22, 23, 24, 27, 30, 31, 34, 41, 42, 45, 47, 49, 50, 52, 53, 57, 58, 59, 60, 61, 68, 71, 72, 74, 76, 77, 79, 82, 83, 85, 86, 90, 92, 93, 94, 97, 99, 100, 101, 102, 104, 105, 107, 110, 111, 112, 113, 114, 115, 119, 120, 121, 122, 124, 126, 127, 130, 133, 134, 137
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OFFSET

1,2


COMMENTS

Note that Dickson refers to C. H. Brooks and S. Watson, 1957 and lists "the following 41 positive integers A<=100." but 47, 53 and 83 are missing.  Michael Somos, Feb 09 2020


REFERENCES

L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 2, p. 475.


LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..1000
H. Mishima, Tables of Representation of concordant number n
K. S. Brown, Concordant Forms


EXAMPLE

From Seiichi Manyama, Jul 15 2019: (Start)
14663^2 + 111384^2 = 112345^2 and 14663^2 + 47*111384^2 = 763751^2. So 47 is a term.
2873161^2 + 2401080^2 = 3744361^2 and 2873161^2 + 83*2401080^2 = 22062761^2. So 83 is a term. (End)
From the K. S. Brown link, 1141^2 + 13260^2 = 13309^2, 1141^2 + 53*13260^2 = 96541^2, is 53 is a term.  Michael Somos, Feb 10 2020


CROSSREFS

Sequence in context: A088769 A057986 A274204 * A105140 A107018 A247868
Adjacent sequences: A306926 A306927 A306928 * A306930 A306931 A306932


KEYWORD

nonn,changed


AUTHOR

N. J. A. Sloane, Mar 16 2019


EXTENSIONS

More terms from Seiichi Manyama, Jul 15 2019


STATUS

approved



