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a(n) = b(n) + d(n), where b(n) = (n-th Lucas number A000204 > 1) and d(n) = (n-th non-Fibonacci number).
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%I #16 Jun 05 2019 03:18:15

%S 7,10,14,20,28,40,59,90,138,215,339,539,862,1384,2229,3594,5802,9374,

%T 15153,24503,39631,64108,103712,167792,271475,439237,710682,1149887,

%U 1860535,3010387,4870886,7881236,12752084,20633281,33385325,54018565,87403848,141422370

%N a(n) = b(n) + d(n), where b(n) = (n-th Lucas number A000204 > 1) and d(n) = (n-th non-Fibonacci number).

%F a(n) = A000204(n+1) + A001690(n), n >= 1. - _N. J. A. Sloane_, Mar 16 2013

%t nn=40;Module[{lcs=LucasL[Range[2,nn+1]],nf,len},nf=Complement[ Range[ nn+ 10],Fibonacci[Range[nn]]];len=Min[Length[lcs],Length[nf]];Total/@ Thread[ {Take[lcs,len],Take[nf,len]}]] (* _Harvey P. Dale_, Mar 16 2013 *)

%Y Cf. A001690, A000204.

%K nonn

%O 1,1

%A _Clark Kimberling_

%E Corrected and extended by _Harvey P. Dale_, Mar 16 2013

%E Offset corrected, cross-references added by _N. J. A. Sloane_, Mar 16 2013