A005371
a(n) = L(L(n)), where L(n) are Lucas numbers A000032.
Original entry on oeis.org
3, 1, 4, 7, 29, 199, 5778, 1149851, 6643838879, 7639424778862807, 50755107359004694554823204, 387739824812222466915538827541705412334749, 19679776435706023589554719270187913247121278789615838446937339578603
Offset: 0
- T. Koshy (2001), Fibonacci and Lucas Numbers with Applications, John Wiley & Sons, New York, 511-516
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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[ Lucas(Lucas(n)): n in [0..20]]; // Vincenzo Librandi, Apr 16 2011
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L:= n-> (<<0|1>, <1|1>>^n. <<2,1>>)[1,1]:
a:= n-> L(L(n)):
seq(a(n), n=0..14); # Alois P. Heinz, Jun 01 2016
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l[n_]:= l[n]= l[n-1] + l[n-2]; l[0]= 2; l[1]= 1; Table[l[l[n]], {n,0,12}]
LucasL[LucasL[Range[0, 15]]] (* G. C. Greubel, Dec 21 2017 *)
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{lucas(n) = fibonacci(n+1) + fibonacci(n-1)};
for(n=0,15, print1(lucas(lucas(n)), ", ")) \\ G. C. Greubel, Dec 21 2017
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[lucas_number2(lucas_number2(n, 1,-1),1,-1) for n in range(15)] # G. C. Greubel Nov 14 2022
More terms from Mario Catalani (mario.catalani(AT)unito.it), Mar 14 2003
Offset changed Feb 28 2007
A123918
a(n) = F(L(n)) - L(F(n)) where F(n) = n-th Fibonacci number and L(n) = n-th Lucas number. Commutator [Fibonacci, Lucas] at n.
Original entry on oeis.org
-1, 0, 1, 0, 9, 78, 2537, 513708, 2971190597, 3416454610154664, 22698374052006551837970693, 173402521172797813159681057129399205126250, 8801063578447437644962364569698707633118370038189051093925447758629
Offset: 0
a(0) = F(L(0)) - L(F(0)) = F(2) - L(0) = 1 - 2 = -1.
a(1) = F(L(1)) - L(F(1)) = F(1) - L(1) = 1 - 1 = 0.
a(2) = F(L(2)) - L(F(2)) = F(3) - L(1) = 2 - 1 = 1.
a(3) = F(L(3)) - L(F(3)) = F(4) - L(2) = 3 - 3 = 0.
a(4) = F(L(4)) - L(F(4)) = F(7) - L(3) = 13 - 4 = 9.
a(5) = F(L(5)) - L(F(5)) = F(11) - L(5) = 89 - 11 = 78.
a(6) = F(L(6)) - L(F(6)) = F(18) - L(8) = 2584 - 47 = 2537.
a(7) = F(L(7)) - L(F(7)) = F(29) - L(13) = 514229 - 521 = 513708.
a(8) = F(L(8)) - L(F(8)) = 2971215073 - 24476 = 2971190597.
a(9) = F(L(9)) - L(F(9)) = 3416454622906707 - 12752043 = 3416454610154664.
a(10) = F(L(10)) - L(F(10)) = 22698374052006863956975682 - 312119004989 = 22698374052006551837970693.
a(11) = F(L(11)) - L(F(11)) = 173402521172797813159685037284371942044301 - 3980154972736918051 = 173402521172797813159681057129399205126250.
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List([0..15], n-> Fibonacci(Lucas(1,-1,n)[2]) - Lucas(1,-1,Fibonacci(n))[2] ); # G. C. Greubel, Aug 06 2019
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[Fibonacci(Lucas(n)) - Lucas(Fibonacci(n)): n in [0..15]]; // G. C. Greubel, Aug 06 2019
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Table[Fibonacci[LucasL[n]]-LucasL[Fibonacci[n]],{n,0,15}] (* Harvey P. Dale, Mar 27 2019 *)
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vector(15, n, n--; f=fibonacci; f(f(n-1)+f(n+1)) - f(f(n)-1) - f(f(n)+1)) \\ G. C. Greubel, Aug 06 2019
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[fibonacci(lucas_number2(n,1,-1)) - lucas_number2(fibonacci(n),1, -1) for n in (0..15)] # G. C. Greubel, Aug 06 2019
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