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...
Length of the longest diagonal in a regular 10-gon with unit side. - Mohammed Yaseen, Nov 12 2020
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
KEYWORD
nonn,cons
AUTHOR
Omar E. Pol, Nov 15 2007
EXTENSIONS
More terms from Jinyuan Wang, Mar 30 2020
STATUS
approved