A083668 -id:A083668 - cp's OEIS frontend

A075737 Prime Fibonacci numbers with prime indices.

2, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497, 1066340417491710595814572169, 19134702400093278081449423917, 475420437734698220747368027166749382927701417016557193662268716376935476241

Offset: 1

Jani Melik, Oct 07 2002

nonn

Same as A005478 except that F(4) = 3 has been omitted.

Sequence of primes in A001519. [James R. Buddenhagen, May 20 2010]

			5 is a prime and fibonacci(5)=5 is also a prime, 7 is a prime and fibonacci(7)=13 is also a prime, but 2 is a prime and fibonacci(2)=1 is not a prime.

T. D. Noe, Table of n, a(n) for n = 1..20

Subsequence of A030426.

Cf. A000045, A005478, A083668, A001519.

with(combinat, fibonacci): fib_supM_pra := proc(n); if (isprime(n)='true') then if (isprime(fibonacci(n))='true') then RETURN(fibonacci(n)); fi; fi; end: seq(fib_supM_pra(i), i=1..500);

Fibonacci[ Prime[ Select[ Range[50], PrimeQ[ Fibonacci[ Prime[ # ]]] & ]]]
Module[{nn=500,fibs},fibs=Fibonacci[Range[nn]];Select[Pick[fibs,Table[ If[ PrimeQ[n],1,0],{n,nn}],1],PrimeQ]] (* Harvey P. Dale, Sep 13 2018 *)

forprime(p=2,1e3,if(isprime(t=fibonacci(p)), print1(t", "))) \\ Charles R Greathouse IV, Feb 03 2014

A119984 Numbers k such that Fibonacci(prime(k)) is prime.

Original entry on oeis.org

2, 3, 4, 5, 6, 7, 9, 10, 14, 15, 23, 32, 33, 72, 83, 84, 87, 97, 104, 105, 429, 637, 710, 1152, 1194, 1692, 2814, 3316, 3824, 3971, 5206, 8002, 10016, 12161, 13681, 18069, 33653, 36467, 48355, 48629, 49455, 73574, 82128, 99005, 123685, 135276, 146779, 210404, 233207, 239581

Offset: 1

Alexander Adamchuk, Aug 04 2006

nonn

All prime Fibonacci numbers have prime indices, except prime F(4) = 3; a(n) is such that Fibonacci(prime(a(n))) is prime. - Robert G. Wilson v, Aug 05 2006

Amiram Eldar, Table of n, a(n) for n = 1..55

Cf. A000045, A000720, A001605, A005478, A030426, A075737, A083668.

Select[ Range@3000, PrimeQ@ Fibonacci@ Prime@ # &] (* Robert G. Wilson v, Aug 05 2006 *)

a(n) = pi(A001605(n+1)). This holds for all n including n=1, since pi(4) = pi(3) = 2. - Jens Kruse Andersen, Jul 24 2014

a(21)-a(27) from Robert G. Wilson v, Aug 05 2006
More terms (from A001605) from T. D. Noe, Aug 18 2006
a(42)-a(48) (from A001605, found by Henri Lifchitz) from Jens Kruse Andersen, Jul 24 2014
a(49)-a(50) (from A001605, found by Henri Lifchitz) from Amiram Eldar, Sep 01 2019

A038672 Primes p such that the p-th Fibonacci number is composite.

Original entry on oeis.org

19, 31, 37, 41, 53, 59, 61, 67, 71, 73, 79, 89, 97, 101, 103, 107, 109, 113, 127, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337

Offset: 1

Jeff Burch

nonn

Hans Havermann, Table of n, a(n) for n = 1..10000
Hans Havermann, Composite Prime-Index Fibonacci Numbers Factored

Cf. A090819 (essentially identical), A083668, A135952.

Rest[Select[Prime[Range[68]], ! PrimeQ[Fibonacci[#]] &]] (* Jayanta Basu, Jul 10 2013 *)
s={A083668}; Complement[Prime[Range[2, 10034]], s] (* Hans Havermann, Feb 12 2014 *)

A122534 Numbers k such that Fibonacci(prime(prime(k))) is prime.

Original entry on oeis.org

1, 2, 3, 4, 9, 23, 25, 1456, 1616, 3865

Offset: 1

Alexander Adamchuk, Sep 18 2006

The corresponding primes are {2,5,89,1597,99194853094755497,...}.
Numbers k such that A093308(k) is prime.
A277575(n) = prime(a(n)) is a prime in A119984.

Cf. A000040, A000045, A119984, A083668, A093308, A075737, A001605, A006450, A005478, A030426, A277284, A277575.

a(n) = PrimePi(A277575(n)) = PrimePi(PrimePi(A277284(n))). - Bobby Jacobs, Oct 26 2016

A286467 Compound filter (prime signature of n & prime signature of the n-th Fibonacci number): a(n) = P(A101296(n), A286545(n)), where P(n,k) is sequence A000027 used as a pairing function.

Original entry on oeis.org

1, 3, 5, 9, 5, 19, 5, 33, 18, 25, 5, 51, 5, 25, 40, 73, 5, 72, 12, 84, 40, 25, 5, 128, 69, 25, 71, 84, 5, 180, 12, 146, 40, 25, 40, 242, 23, 40, 40, 198, 12, 180, 5, 177, 177, 40, 5, 337, 31, 216, 40, 84, 12, 284, 59, 308, 140, 40, 12, 478, 12, 40, 177, 339, 40, 180, 23, 177, 140, 387, 12, 610, 12, 59, 216, 177, 59, 309, 12, 540, 332, 40, 5, 608, 59, 40, 59

Offset: 1

Antti Karttunen, May 17 2017

nonn

Nonsquare semiprimes pq for which F(pq) is also a semiprime is given by the positions where 25's occur in this sequence: 10, 14, 22, 26, 34, 94, (any more terms?). This is a subsequence of A072381.

Antti Karttunen, Table of n, a(n) for n = 1..1300 (based also on the b-file of A278245 provided by Hans Havermann)

Cf. A000027, A046523, A072381, A101296, A278245, A286545.

Cf. A083668 (positions of 5's).

(define (A286467 n) (* (/ 1 2) (+ (expt (+ (A101296 n) (A286545 n)) 2) (- (A101296 n)) (- (* 3 (A286545 n))) 2)))

a(n) = (1/2)*(2 + ((A101296(n) + A286545(n))^2) - A101296(n) - 3*A286545(n)).

A277284 Prime-indexed primes p such that Fibonacci(p) is prime.

Original entry on oeis.org

3, 5, 11, 17, 83, 431, 509, 130021, 148091, 433781

Offset: 1

Bobby Jacobs, Oct 21 2016

Intersection of A006450 and A083668. - Michel Marcus, Oct 21 2016

			17 = A000040(7), with 7 itself being a prime, and A000045(17) = 1597, a prime, thus 17 is included in this sequence.

Cf. A000040, A000045, A006450, A083668, A122534, A277575.

Select[Prime[Prime[Range[37000]]],PrimeQ[Fibonacci[#]]&] (* Harvey P. Dale, Sep 12 2019 *)

isok(p) = isprime(p) && isprime(primepi(p)) && isprime(fibonacci(p)); \\ Michel Marcus, Oct 21 2016

a(n) = prime(A277575(n)).

a(n) = prime(prime(A122534(n))).

A277575 Primes p such that Fibonacci(prime(p)) is prime.

Original entry on oeis.org

2, 3, 5, 7, 23, 83, 97, 12161, 13681, 36467

Offset: 1

Bobby Jacobs, Oct 20 2016

Suggested by Alexander Adamchuk in A122534.

Primes in A119984.

Cf. A000040, A000045, A001605, A005478, A006450, A030426, A075737, A083668, A093308, A122534, A277284.

isok(p) = isprime(p) && isprime(fibonacci(prime(p))); \\ Michel Marcus, Oct 22 2016

a(n) = prime(A122534(n)).

a(n) = PrimePi(A277284(n)).

A117517 Numbers k such that F(2*k + 1) is prime where F(m) is a Fibonacci number.

Original entry on oeis.org

1, 2, 3, 5, 6, 8, 11, 14, 21, 23, 41, 65, 68, 179, 215, 216, 224, 254, 284, 285, 1485, 2361, 2693, 4655, 4838, 7215, 12780, 15378, 17999, 18755, 25416, 40919, 52455, 65010, 74045, 100553, 198689, 216890, 295020, 296844, 302355, 465758, 524948, 642803, 818003, 901529, 984360, 1452176

Offset: 1

Parthasarathy Nambi, Apr 26 2006

nonn

For F(k) to be prime, with k > 4, it is necessary but not sufficient for k to be prime. Hence after F(4) = 3, every prime F(m) is of the form F(2*k+1) for some k. Every prime divides some Fibonacci number. See also comment to A093062. - Jonathan Vos Post, Apr 29 2006

			If k=68 then F(2*k + 1) = 19134702400093278081449423917, a prime, so 68 is a term.

H. Dubner and W. Keller, New Fibonacci and Lucas Primes, Math. Comp. 68 (1999) 417-427.

Cf. A000045, A001605, A117595.

Cf. A001602, A022307, A030427, A051694, A075737, A083668, A099000.

[n: n in [0..1000] | IsPrime(Fibonacci(2*n+1))]; // Vincenzo Librandi, May 24 2016

Select[Range[0, 5000], PrimeQ[Fibonacci[2 # + 1]] &] (* Vincenzo Librandi, May 24 2016 *)

a(n) = (A083668(n)-1)/2. - R. J. Mathar, Jul 08 2009

a(n) = (A001605(n+1)-1)/2, n > 1. - Vincenzo Librandi, May 24 2016

More terms from Vincenzo Librandi, May 24 2016

cp's OEIS Frontend

A075737 Prime Fibonacci numbers with prime indices.

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A119984 Numbers k such that Fibonacci(prime(k)) is prime.

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A038672 Primes p such that the p-th Fibonacci number is composite.

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A122534 Numbers k such that Fibonacci(prime(prime(k))) is prime.

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A286467 Compound filter (prime signature of n & prime signature of the n-th Fibonacci number): a(n) = P(A101296(n), A286545(n)), where P(n,k) is sequence A000027 used as a pairing function.

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A277284 Prime-indexed primes p such that Fibonacci(p) is prime.

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A277575 Primes p such that Fibonacci(prime(p)) is prime.

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A117517 Numbers k such that F(2*k + 1) is prime where F(m) is a Fibonacci number.

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