OFFSET
1,1
COMMENTS
In a regular pentagon, inscribed in a unit circle this equals twice the largest distance between a vertex and a midpoint of a side.
This is an integer in the quadratic number field Q(sqrt(5)).
Only the first digit differs from A001622.
LINKS
Sumit Kumar Jha, Two complementary relations for the Rogers-Ramanujan continued fraction, arXiv:2112.12081 [math.NT], 2021.
FORMULA
From Christian Katzmann, Mar 19 2018: (Start)
Equals Sum_{n>=0} (15*(2*n)!+40*n!^2)/(2*n!^2*3^(2*n+2)).
Equals 5/2 + Sum_{n>=0} 5*(2*n)!/(2*n!^2*3^(2*n+1)). (End)
Constant c = 2 + 2*cos(2*Pi/10). The linear fractional transformation z -> c - c/z has order 10, that is, z = c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(c - c/(z)))))))))). - Peter Bala, May 09 2024
EXAMPLE
3.618033988749894848204586834365638117720309179805762862135448622705260462...
MATHEMATICA
First@ RealDigits[2 + GoldenRatio, 10, 77] (* Michael De Vlieger, Jan 13 2018 *)
PROG
(PARI) (5 + sqrt(5))/2 \\ Altug Alkan, Mar 19 2018
CROSSREFS
KEYWORD
AUTHOR
Wolfdieter Lang, Jan 08 2018
STATUS
approved