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A216869 The smallest non-constant arithmetic progression of integer squares of maximal length three. 4
1, 25, 49 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Bremner (2012): "Euler showed that the length of the longest arithmetic progression (AP) of integer squares is equal to three. [See Dickson.] Xarles (2011) investigated APs in number fields, and proved the existence of an upper bound K(d) for the maximal length of an AP of squares in a number field of degree d. He shows that K(2) = 5." See A216870.

REFERENCES

L. E. Dickson, History of the Theory of Numbers, Vol. II, Chelsea, New York, 1952, pp. 435-440.

LINKS

Table of n, a(n) for n=1..3.

A. Alvarado and E. H. Goins, Arithmetic progressions on conic sections, arXiv 2012.

A. Bremner, Arithmetic progressions of squares in cubic fields, Abstract 2012.

FORMULA

a(2) - a(1) = a(3) - a(2) = 24.

EXAMPLE

a(1) = 1^2, a(2) = 5^2, a(3) = 7^2.

CROSSREFS

Cf. A216870, A221671, A221672.

Sequence in context: A038811 A028505 A154082 * A143278 A106632 A284666

Adjacent sequences:  A216866 A216867 A216868 * A216870 A216871 A216872

KEYWORD

nonn,fini,full,bref

AUTHOR

Jonathan Sondow, Nov 20 2012

STATUS

approved

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Last modified April 8 13:35 EDT 2020. Contains 333314 sequences. (Running on oeis4.)