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 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. 4
 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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 20 09:56 EDT 2019. Contains 326143 sequences. (Running on oeis4.)