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 A280106 Numbers k such that the half sum of the prime factors of Fibonacci(k) is a Fibonacci number. 0
 3, 6, 8, 10, 14, 15, 22, 26, 30, 34, 94 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Or numbers k such that A080648(k)/2 is a Fibonacci number. Is this sequence finite ? a(12), if it exists is >5000. - Robert Price, Mar 02 2017 LINKS EXAMPLE 10 is in the sequence because Fibonacci(10) = 5*11=> 5+11 = 2*8 = 2*F(6); 94 is in the sequence because Fibonacci(94) = 2971215073*6643838879 => 2971215073+6643838879 = 2*4807526976 = 2*F(48). MAPLE with(numtheory):with(combinat, fibonacci):nn:=300: for n from 3 to nn do:   f:=fibonacci(n):x:=factorset(f):n0:=nops(x):   s:=sum(‘x[i]’, ‘i’=1..n0):c:=s/2:   x1:=sqrt(5*c^2-4):x2:=sqrt(5*c^2+4):     if x1=floor(x1) or x2=floor(x2)      then      print(n):      else     fi: od: CROSSREFS Cf. A000045, A080648. Sequence in context: A072149 A001066 A099518 * A184855 A187336 A169582 Adjacent sequences:  A280103 A280104 A280105 * A280107 A280108 A280109 KEYWORD nonn,more AUTHOR Michel Lagneau, Dec 28 2016 STATUS approved

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Last modified July 30 13:24 EDT 2021. Contains 346359 sequences. (Running on oeis4.)