A244596 Decimal expansion of the coefficient D appearing in the asymptotic evaluation of P_a(n), the number of primitive Pythagorean triples whose area does not exceed a given bound n.

2, 9, 7, 4, 6, 1, 5, 5, 2, 9, 8, 1, 2, 6, 0, 1, 8, 8, 9, 7, 1, 4, 6, 2, 4, 0, 2, 2, 7, 0, 1, 4, 7, 6, 7, 9, 8, 3, 2, 8, 4, 7, 0, 5, 4, 2, 2, 9, 5, 5, 1, 1, 9, 6, 7, 2, 9, 6, 7, 1, 7, 3, 8, 8, 4, 0, 1, 9, 8, 2, 4, 7, 7, 9, 3, 1, 0, 5, 0, 5, 0, 4, 1, 8, 4, 7, 9, 9, 6, 7, 4, 2, 4, 2, 2, 8, 0, 1, 4, 5, 0, 7, 4

Offset: 0

Author

Jean-François Alcover, Jul 01 2014

Keywords

• nonn
• cons
• easy

Examples

			0.2974615529812601889714624022701476798328470542295511967296717388401982...
		

References

• Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 5.2 Pythagorean Triple Constants, p. 277.

Links

• Eric Weisstein's MathWorld, Primitive Pythagorean Triple

Crossrefs

Cf. A242439.

Programs

Mathematica

-((1 + 1/2^(1/3))*Zeta[1/3]/((1 + 1/4^(1/3))*Zeta[4/3])) // RealDigits[#, 10, 103]& // First

Formula

P_a(n) = C*n^(1/2) - D*n^(1/3) + O(n^(1/4)*log(n)).

D = -((1 + 1/2^(1/3))*zeta(1/3)/((1 + 1/4^(1/3))*zeta(4/3))).