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

0,1

References

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

Links

Table of n, a(n) for n=0..102.

Eric Weisstein's MathWorld, Primitive Pythagorean Triple

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))).

Example

0.2974615529812601889714624022701476798328470542295511967296717388401982...

Mathematica

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

Crossrefs

Cf. A242439.

Sequence in context: A254140 A200991 A013500 * A309928 A176977 A202473

Adjacent sequences: A244593 A244594 A244595 * A244597 A244598 A244599

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jul 01 2014

Status

approved