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a(n) = b(n) + d(n), where b(n) = (n-th Fibonacci number > 1) and d(n) = (n-th non-Fibonacci number).
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%I #18 Jun 04 2019 22:53:57

%S 6,9,12,17,23,32,46,69,104,160,250,395,629,1007,1619,2607,4205,6790,

%T 10972,17738,28685,46397,75055,121424,196450,317844,514264,832076,

%U 1346306,2178347,3524617,5702927,9227506,14930394,24157860,39088213

%N a(n) = b(n) + d(n), where b(n) = (n-th Fibonacci number > 1) and d(n) = (n-th non-Fibonacci number).

%F a(n) = A000045(n+2)+A001690(n). - _R. J. Mathar_, Feb 01 2019

%t nn = 36; b = Table[Fibonacci[n + 2], {n, nn}]; d = Take[Complement[Range[2, 2*nn], b], nn]; b + d (* _T. D. Noe_, Mar 09 2011 *)

%t fibs=Select[Fibonacci[Range[60]], #>1&]; nonfibs=Take[Complement[Range[4,75], fibs], Length[fibs]]; Total/@Thread[{fibs,nonfibs}] (* _Harvey P. Dale_, Mar 10 2011 *)

%K nonn

%O 1,1

%A _Clark Kimberling_.