A094884 Decimal expansion of phi/sqrt(2), where phi = (1+sqrt(5))/2.

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

Offset

1,3

Comments

An algebraic number with minimal polynomial 4*x^4 - 6*x^2 + 1. - Charles R Greathouse IV, Mar 25 2014

Links

Ivan Panchenko, Table of n, a(n) for n = 1..1000

Formula

Equals Product_{k>=0} (1 + (-1)^k/(10*k+5)). - Amiram Eldar, Nov 23 2024

Equals A094887/2 = sqrt(A239798). - Hugo Pfoertner, Nov 23 2024

Example

1.144122805635368595200145567160604153072306753675541225...

Mathematica

RealDigits[GoldenRatio/Sqrt[2], 10, 120][[1]] (* Harvey P. Dale, Feb 11 2015 *)

Prog

(PARI) sqrt(sqrt(5)+3)/2 \\ Charles R Greathouse IV, Mar 25 2014
(Magma) SetDefaultRealField(RealField(100)); R:= RealField(); (1+Sqrt(5) )/(2*Sqrt(2)); // G. C. Greubel, Sep 27 2018

Crossrefs

Cf. A001622 (phi), A002193 (sqrt(2)), A017329, A094887, A239798.

Sequence in context: A128433 A089746 A225330 * A359532 A281540 A053216

Adjacent sequences: A094881 A094882 A094883 * A094885 A094886 A094887

Keyword

cons,nonn

Author

N. J. A. Sloane, Jun 15 2004

Status

approved