A256367 Decimal expansion of sec(phi), a constant related to the "broadworm" (or "caliper") problem.

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

Offset

1,3

Comments

A cubic number of denominator 3 and minimal polynomial 3x^6 + 36x^4 + 16x^2 - 64. - Charles R Greathouse IV, May 13 2019

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.4 Moser's Worm Constant, pp. 493-494.

Links

Table of n, a(n) for n=1..103.

J.-F. Alcover, Figure 8.3 A caliper. [after Steven Finch]

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 63.

Steven R. Finch and John E. Wetzel, Lost in a Forest

Index entries for algebraic numbers, degree 3

Formula

Sec(phi) = 1/sqrt(1 - (1/6 + (4/3)*sin((1/3)*arcsin(17/64)))^2), which is the positive root of 3*x^6 + 36*x^4 + 16*x^2 - 64.

Example

1.0435901095949847538118417712870227333548896969340378971...

Mathematica

RealDigits[Root[3*x^6 + 36*x^4 + 16*x^2 - 64, x, 2], 10, 103] // First

Prog

(PARI) polrootsreal(3*x^6 + 36*x^4 + 16*x^2 - 64)[2] \\ Charles R Greathouse IV, May 13 2019

Crossrefs

Cf. A240969, A244046.

Sequence in context: A236360 A299323 A010475 * A242910 A200350 A227684

Adjacent sequences: A256364 A256365 A256366 * A256368 A256369 A256370

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Mar 26 2015

Status

approved