A355674 Decimal expansion of 1351/780.

1, 7, 3, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2, 0, 5, 1, 2, 8, 2

Offset

1,2

Comments

This constant is the greater limit to the value of sqrt(3) used by Archimedes in the calculation of Pi.

References

William Dunham, Journey Through Genius, Wiley, 1990, Chapter 3, p. 98.

Ernst Sondheimer and Alan Rogerson, Numbers and Infinity, Cambridge University Press, 1981, p. 97.

Links

Table of n, a(n) for n=1..88.

Kevin Brown, Archimedes and the square root of 3, MathPages.

Index entries for algebraic numbers, degree 1.

Index entries for linear recurrences with constant coefficients, signature (1,-1,1,-1,1).

Formula

From Chai Wah Wu, Apr 18 2024: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n > 8.

G.f.: x*(-5*x^7 + 10*x^6 - 10*x^5 + 5*x^4 - 5*x^3 + 3*x^2 - 6*x - 1)/((x - 1)*(x^2 - x + 1)*(x^2 + x + 1)). (End)

Example

1.732051282051282051282051282051282051282...

Mathematica

First[RealDigits[N[1351/780, 88]]]

Crossrefs

Cf. A002194, A355673 (lesser limit), essentially the same as A021316.

Sequence in context: A355673 A160390 A002194 * A256843 A033327 A024584

Adjacent sequences: A355671 A355672 A355673 * A355675 A355676 A355677

Keyword

nonn,cons,easy

Author

Stefano Spezia, Jul 14 2022

Status

approved