A134945 Decimal expansion of 1 + sqrt(5).

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

Offset

1,1

Comments

If "index" equals (0,2) then this sequence is the decimal expansion of (golden ratio divided by 5 = phi/5 = (1 + sqrt(5))/10). Example: 0.323606797...

Apart from the leading digit the same as A134972, A098317 and A002163. - R. J. Mathar, Aug 06 2013

Length of the longest diagonal in a regular 10-gon with unit side. - Mohammed Yaseen, Nov 12 2020

Abscissa of the first superstable point of the logistic map (see Finch). - Stefano Spezia, Nov 23 2024

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.9, p. 66.

Links

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

Index entries for algebraic numbers, degree 2.

Formula

From Christian Katzmann, Mar 19 2018: (Start)

Equals Sum_{n>=0} (15*(2*n)!+8*n!^2)/(n!^2*3^(2*n+2)).

Equals 1 + Sum_{n>=0} 5*(2*n)!/(n!^2*3^(2*n+1)). (End)

Equals 1/A019827. - R. J. Mathar, Jan 17 2021

Equals Product_{k>=1} (1 + 1/Fibonacci(2*k)). - Amiram Eldar, May 27 2021

Example

3.2360679774997896964...

Mathematica

RealDigits[1 + Sqrt[5], 10, 100][[1]] (* Michael De Vlieger, Nov 13 2020 *)

Prog

(PARI) 1 + sqrt(5) \\ Altug Alkan, Mar 19 2018

Crossrefs

Cf. A000045, A002163, A098317, A134972.

Sequence in context: A175717 A051701 A225696 * A256185 A343368 A021313

Adjacent sequences: A134942 A134943 A134944 * A134946 A134947 A134948

Keyword

nonn,cons

Author

Omar E. Pol, Nov 15 2007

Extensions

More terms from Jinyuan Wang, Mar 30 2020

Status

approved