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 A030426 a(n) = Fibonacci(prime(n)). 22
 1, 2, 5, 13, 89, 233, 1597, 4181, 28657, 514229, 1346269, 24157817, 165580141, 433494437, 2971215073, 53316291173, 956722026041, 2504730781961, 44945570212853, 308061521170129, 806515533049393, 14472334024676221, 99194853094755497, 1779979416004714189 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Except for Fibonacci(4) = 3, if Fibonacci(n) is prime, then n is also prime. However, if n is prime, Fibonacci(n) might be composite, as, for example, Fibonacci(19) = 4181 = 37 * 113. - Alonso del Arte, Jan 28 2014 The values are pairwise relatively prime because gcd(Fib(m), Fib(n)) = Fib(gcd(m, n)) and this equals Fib(1) = 1 when m!=n are prime numbers. - Lee A. Newberg, May 05 2023 LINKS Alois P. Heinz, Table of n, a(n) for n = 1..642 (first 100 terms from T. D. Noe) Michel Bataille, Problem 90.G, Problem Corner, The Mathematical Gazette, Vol. 90, No. 518 (2006), p. 354; Solution, ibid., Vol. 91, No. 520 (2007), pp. 160-161. FORMULA a(n) = A000045(A000040(n)). From Jianing Song, Dec 26 2018: (Start) a(n) == 1 (mod prime(n)) if prime(n) == 1, 4 (mod 5). a(n) == -1 (mod prime(n)) if prime(n) == 2, 3 (mod 5). (End) a(n) == Sum_{k=0..floor((prime(n)-1)/2)} (-1)^k * binomial(2*k,k) (mod prime(n)) (Bataille, 2006). - Amiram Eldar, Jul 02 2023 MAPLE with(combinat); for i from 1 to 50 do fibonacci(ithprime(i)); od; # second Maple program: a:= n-> (<<0|1>, <1|1>>^ithprime(n))[1, 2]: seq(a(n), n=1..30); # Alois P. Heinz, Jan 20 2017 MATHEMATICA Fibonacci[Prime[Range[30]]] (* Harvey P. Dale, Mar 25 2013 *) PROG (PARI) a(n)=fibonacci(prime(n)) \\ Charles R Greathouse IV, Apr 26 2012 (Magma) [Fibonacci(NthPrime(n)): n in [1..80]]; // Vincenzo Librandi, May 22 2015 (GAP) a:=List(Filtered([1..100], IsPrime), i->Fibonacci(i));; Print(a); # Muniru A Asiru, Dec 29 2018 CROSSREFS Cf. A000040, A000045, A005478. Sequence in context: A325626 A325627 A075736 * A075742 A075737 A100843 Adjacent sequences: A030423 A030424 A030425 * A030427 A030428 A030429 KEYWORD nonn,easy,nice AUTHOR John C. Hallyburton, Jr. (jhallyburton(AT)mx1.AspenRes.Com) STATUS approved

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Last modified August 10 05:56 EDT 2024. Contains 375044 sequences. (Running on oeis4.)