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

0,3

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

Table of n, a(n) for n=0..41.

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

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

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

Sequence in context: A210658 A143122 A093067 * A159931 A159755 A215534

Adjacent sequences: A098119 A098120 A098121 * A098123 A098124 A098125

Keyword

nonn

Author

James R. Buddenhagen, Sep 24 2004

Status

approved