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%I #39 May 27 2021 06:24:44
%S 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,
%T 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,
%U 2,0,9,2,5,6,3,7,8,0,4,8,9,9,4,1,4,4,1,4
%N Decimal expansion of 1 + sqrt(5).
%C 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...
%C Apart from the leading digit the same as A134972, A098317 and A002163. - _R. J. Mathar_, Aug 06 2013
%C Length of the longest diagonal in a regular 10-gon with unit side. - _Mohammed Yaseen_, Nov 12 2020
%F From _Christian Katzmann_, Mar 19 2018: (Start)
%F Equals Sum_{n>=0} (15*(2*n)!+8*n!^2)/(n!^2*3^(2*n+2)).
%F Equals 1 + Sum_{n>=0} 5*(2*n)!/(n!^2*3^(2*n+1)). (End)
%F Equals 1/A019827. - _R. J. Mathar_, Jan 17 2021
%F Equals Product_{k>=1} (1 + 1/Fibonacci(2*k)). - _Amiram Eldar_, May 27 2021
%e 3.2360679774997896964...
%t RealDigits[1 + Sqrt[5], 10, 100][[1]] (* _Michael De Vlieger_, Nov 13 2020 *)
%o (PARI) 1 + sqrt(5) \\ _Altug Alkan_, Mar 19 2018
%Y Cf. A000045, A002163, A098317, A134972.
%K nonn,cons
%O 1,1
%A _Omar E. Pol_, Nov 15 2007
%E More terms from _Jinyuan Wang_, Mar 30 2020
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