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Decimal expansion of the number 4.1636635147332912770473687837946011358... having continued fraction expansion 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, ... (arithmetical average of two consecutive odd primes A024675).
6

%I #5 Jul 09 2023 19:30:57

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

%T 1,3,5,8,0,5,7,6,4,4,9,7,4,6,3,7,4,3,9,6,9,1,5,9,0,3,6,9,5,1,4,8,8,9,

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

%N Decimal expansion of the number 4.1636635147332912770473687837946011358... having continued fraction expansion 4, 6, 9, 12, 15, 18, 21, 26, 30, 34, 39, ... (arithmetical average of two consecutive odd primes A024675).

%t a = {}; Do[AppendTo[a, (Prime[n] + Prime[n + 1])/2], {n, 2, 500}]; RealDigits[N[FromContinuedFraction[a], 100]][[1]]

%Y Cf. A064442, A127549, A127550, A127551, A127552, A127553, A127555, A127556, A127557, A127558, A127559, A024675.

%K cons,nonn

%O 1,1

%A _Artur Jasinski_, Jan 18 2007

%E a(100) corrected by _Sean A. Irvine_, Jul 09 2023