OFFSET
0,3
COMMENTS
(a(4*n),a(4*n+1)) are legs of the unique Pythagorean right triangle with hypotenuse 5^n and relatively prime legs.
REFERENCES
Jacobi, C. G. J. (1829) Fundamenta Nova Theoriae Functionum Ellipticarum, Regiomonti, Sumptibus fratrum Borntraeger; reprinted in Jacobi, C. G. J. (1881-1891) Gesammelte Werke (Reimer, Berlin), Vol. 1, pp. 49-239 [reprinted (1969) by Chelsea, New York; now distributed by Am. Mathematical Soc., Providence, RI].
LINKS
Elias M. Stein and Rami Shakarchi, Complex Analysis, Ch. 10.
Eric Weisstein's World of Mathematics, Sum of Squares Function
EXAMPLE
(a(2*3),a(2*3+1)) = (2,11) because (2,11) are (even,odd), relatively prime and 2^2 + 11^2 = 5^3. There is just one such pair.
CROSSREFS
KEYWORD
nonn
AUTHOR
James R. Buddenhagen, Sep 24 2004
STATUS
approved