

A216869


The smallest nonconstant arithmetic progression of integer squares of maximal length three.


4




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. 435440.


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



