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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 20 04:44 EST 2020. Contains 332063 sequences. (Running on oeis4.)