A098122 Let (A,B)=(a(2*n),a(2*n+1)), then (A,B) is (even,odd), gcd(A,B)=1 and A^2 + B^2 = 5^n. Note: a(0)=0.

0, 1, 2, 1, 4, 3, 2, 11, 24, 7, 38, 41, 44, 117, 278, 29, 336, 527, 718, 1199, 3116, 237, 2642, 6469, 10296, 11753, 33802, 8839, 16124, 76443, 136762, 108691, 354144, 164833, 24478, 873121, 1721764, 922077, 3565918, 2521451, 1476984, 9653287

Offset: 0

Author

James R. Buddenhagen, Sep 24 2004

Keywords

• nonn

Comments

(a(4*n),a(4*n+1)) are legs of the unique Pythagorean right triangle with hypotenuse 5^n and relatively prime legs.

Examples

			(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.
		

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.
• XIAO Gang, Two Squares (a section of WWW Interactive Multipurpose Server)
• Eric Weisstein's World of Mathematics, Sum of Squares Function

Crossrefs

Cf. A006495, A006496 (the odd and even numbers separately).