A103114 - OEIS

%I #10 Dec 08 2022 07:36:22

%S 1,2,1,7,0,5,19,2,23,87,0,87,377,0,379,1599,2,1599,6765,2,6765,28657,

%T 2,28655,121391,2,121393,514231,0,514229,2178307,2,2178311,9227463,0,

%U 9227463,39088169,0,39088171,165580143,2,165580143,701408733,2

%N a(n) = abs( f(Fibonacci(n)) - Fibonacci(f(n)) ), where f(n) = n-2 if (n mod 3) = 0, f(n) = n+2 if (n mod 3) = 1, otherwise f(n) = n.

%H G. C. Greubel, <a href="/A103114/b103114.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = abs( f(Fibonacci(n)) - Fibonacci(f(n)) ), where f(n) = n-2 if (n mod 3) = 0, f(n) = n+2 if (n mod 3) = 1, otherwise f(n) = n; or f(n) = - f(n-1) - f(n-2) + 3*(n-1), with f(1) = 3 and f(2) = 2.

%t f[n_]= If[Mod[n,3]==0, n-2, If[Mod[n,3]==1, n+2, n]];

%t a[n_]:= Abs[f[Fibonacci[n]] - Fibonacci[f[n]]];

%t Table[a[n], {n, 50}]

%o (Magma)

%o f:= func< n | n mod 3 eq 0 select n-2 else n mod 3 eq 1 select n+2 else n >;

%o A103114:= func< n | Abs( f(Fibonacci(n)) - Fibonacci(f(n)) ) >;

%o [A103114(n): n in [1..60]]; // _G. C. Greubel_, Dec 06 2022

%o (SageMath)

%o def f(n):

%o     if (n%3)==0: return n-2

%o     elif (n%3)==1: return n+2

%o     else: return n

%o def A103114(n): return abs( f(fibonacci(n)) - fibonacci(f(n)) )

%o [A103114(n) for n in range(1,60)] # _G. C. Greubel_, Dec 06 2022

%K nonn,easy,less

%O 1,2

%A _Roger L. Bagula_, Mar 16 2005

%E Edited by _G. C. Greubel_, Dec 06 2022