A138337 Positions of digits after decimal point of number Pi where the approximation to the number Pi by a root of a polynomial of 3 degree does not improve the accuracy.

7, 13, 17, 30, 37, 48, 62, 63, 77, 81, 86, 92, 97, 114, 117, 125, 129, 143, 148, 152, 156, 159, 168, 174, 180, 185, 196, 200, 204, 211, 227, 235, 244, 247, 259, 266, 267, 282

Offset

1,1

Comments

If there is a set of consecutive numbers in this sequence starting at k, this means that k-1 is a good approximation to Pi.

If the set of successive integers is longer that approximation k-1 better (see A138338)

Links

Table of n, a(n) for n=1..38.

Example

a(1)=7 because 3.141593 (6 digits) is root of cubic 2 + 29 x - 22 x^2 + 4 x^3 and 3.1415927 (7 digits) also is root of that same polynomial -3061495+674903*x+95366*x^2

Mathematica

b = {}; a = {}; Do[k = Recognize[N[Pi, n + 1], 3, x]; If[MemberQ[a, k], AppendTo[b, n], AppendTo[a, k]], {n, 2, 300}]; b

Crossrefs

Cf. A138335, A138336, A138338.

Sequence in context: A154408 A089531 A247010 * A359063 A174877 A230433

Adjacent sequences: A138334 A138335 A138336 * A138338 A138339 A138340

Keyword

nonn,uned,base

Author

Artur Jasinski, Mar 15 2008

Status

approved