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%I #18 Mar 11 2024 05:48:51
%S 1,1,2,3,5,13,89,233,1597,28657,514229,433494437,2971215073,
%T 99194853094755497,1066340417491710595814572169,
%U 19134702400093278081449423917
%N Fibonacci numbers whose sum of proper divisors is also a Fibonacci number.
%C Fibonacci numbers k such that A001065(k) is a Fibonacci number.
%C A001065(a(n)) is a Fibonacci number.
%C Certainly this contains 1 and the terms of A005478. Does it contain any other terms? - _R. J. Mathar_, Sep 17 2009
%C The next term, Fibonacci(359) = 4.754...*10^74, is too large to include in the data section. There are no composite Fibonacci numbers below A000045(1423) in this sequence. - _Amiram Eldar_, Mar 11 2024
%p isA000045 := proc(n) local i,f ; for i from 0 do f := combinat[fibonacci](i) ; if f = n then RETURN(true) ; elif f > n then RETURN(false) ; fi ; od; end: A001065 := proc(n) numtheory[sigma](n)-n ; end: isA139095 := proc(n) RETURN( isA000045(n) and isA000045(A001065(n)) ) ; end: for i from 1 to 230 do if isA139095(combinat[fibonacci](i)) then printf("%d,", combinat[fibonacci](i)) ; fi ; od: # _R. J. Mathar_, May 22 2008
%Y Cf. A000045, A001065, A005478, A074283, A139589.
%K nonn
%O 1,3
%A _Omar E. Pol_, May 11 2008
%E More terms from _R. J. Mathar_, May 22 2008
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