A135957 a(n) = smallest k such that Fibonacci(prime(k)) has exactly n prime factors.
1, 2, 8, 12, 25, 50, 96, 73, 164
Offset: 0
Extensions
Edited and extended by David Wasserman, Mar 26 2008
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(2) = 150 = 37+113 because A050937(2) = 4181 = 37*113. a(3) = 2974 = 557 + 2417 because A050937(3) = 1346269 = 557*2417.
k = {}; Do[If[ ! PrimeQ[Fibonacci[Prime[n]]], b = FactorInteger[Fibonacci[Prime[n]]]; c =Length[FactorInteger[b]]; d = 0; Do[d = d + b[[r]][[1]], {r, 1, c}]; AppendTo[k, d]], {n, 1, 50}]; k
a(3) = 24157817 because 24157817 is the smallest Fibonacci number with a prime index (that is, 37) which has 3 prime factors (24157817 = 73*149*2221).
Transpose[Flatten[Table[Select[{#, PrimeOmega[#]}&/@Fibonacci[Prime[Range[50]]], Last[#]==n&,1], {n, 5}], 1]][[1]] (* To generate the first 6 terms, change 50 to 100 inside Range and change 5 to 6 for the upper limit of n. *) (* Harvey P. Dale, Jun 20 2013 *)
a(1) = 150 = 37+113 because A135953(1) = 4181 = 37*113. a(2) = 2974 = 557+2417 because A135953(2) = 1346269 = 557*2417.
k = {}; Do[If[ ! PrimeQ[Fibonacci[Prime[n]]], b = FactorInteger[Fibonacci[Prime[n]]]; c = Length[FactorInteger[b]]; If[c == 2, d = b[[1]][[1]] + b[[2]][[1]]; AppendTo[k, d]]], {n, 1, 50}]; k
Total[Transpose[FactorInteger[#]][[1]]]&/@Select[Fibonacci[Prime[ Range[50]]], PrimeOmega[#]==2&] (* Harvey P. Dale, Feb 18 2012 *)
k = {}; Do[If[PrimeQ[2^n - 1], AppendTo[k, Fibonacci[2^n - 1]]], {n, 1, 15}]; k
Fibonacci/@Select[Table[2^Prime[n]-1,{n,5}],PrimeQ] (* Harvey P. Dale, May 06 2018 *)
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