A001602 -id:A001602 - cp's OEIS frontend

A051694 Smallest Fibonacci number that is divisible by n-th prime.

2, 3, 5, 21, 55, 13, 34, 2584, 46368, 377, 832040, 4181, 6765, 701408733, 987, 196418, 591286729879, 610, 72723460248141, 190392490709135, 24157817, 8944394323791464, 160500643816367088, 89, 7778742049, 12586269025

Offset: 1

N. J. A. Sloane

It is conjectured that a(n) is not divisible by prime(n)^2. See Remark on p. 528 of Wall and Conjectures in CNRS links. - Michel Marcus, Feb 24 2016

			55 is first Fibonacci number that is divisible by 11, the 5th prime, so a(5) = 55.

Alois P. Heinz, Table of n, a(n) for n = 1..650 (first 100 terms from Zak Seidov)
Shalom Eliahou, Mystères Arithmétiques de la Suite de Fibonacci, (in French), Images des Mathématiques, CNRS, 2014.
Ron Knott, Fibonacci numbers with tables of F(0)-F(500)
D. D. Wall, Fibonacci series modulo m, Amer. Math. Monthly, 67 (1960), 525-532.

Cf. A000045, A001602, A001605, A005478.

F:= proc(n) option remember; `if`(n<2, n, F(n-1)+F(n-2)) end:
a:= proc(n) option remember; local p, k; p:=ithprime(n);
      for k while irem(F(k), p)>0 do od; F(k)
    end:
seq(a(n), n=1..30);  # Alois P. Heinz, Sep 28 2015

f[n_] := Block[{fib = Fibonacci /@ Range[n^2]}, Reap@ For[k = 1, k <= n, k++, Sow@ SelectFirst[fib, Mod[#, Prime@ k] == 0 &]] // Flatten //
Rest]; f@ 26 (* Michael De Vlieger, Mar 28 2015, Version 10 *)

a(n)=if(n==3,5,my(p=prime(n));fordiv(p^2-1,d,if(fibonacci(d)%p==0, return(fibonacci(d))))) \\ Charles R Greathouse IV, Jul 17 2012

a(n) = A000045(A001602(n)). - Max Alekseyev, Dec 12 2007

log a(n) << (n log n)^2. - Charles R Greathouse IV, Jul 17 2012

More terms from Jud McCranie

More terms from James Sellers, Dec 08 1999

A001612 a(n) = a(n-1) + a(n-2) - 1 for n > 1, a(0)=3, a(1)=2.

Original entry on oeis.org

3, 2, 4, 5, 8, 12, 19, 30, 48, 77, 124, 200, 323, 522, 844, 1365, 2208, 3572, 5779, 9350, 15128, 24477, 39604, 64080, 103683, 167762, 271444, 439205, 710648, 1149852, 1860499, 3010350, 4870848, 7881197, 12752044, 20633240, 33385283, 54018522

Offset: 0

N. J. A. Sloane

a(n+3) = A^(n)B^(2)(1), n >= 0, with compositions of Wythoff's complementary A(n):=A000201(n) and B(n)=A001950(n) sequences. See the W. Lang link under A135817 for the Wythoff representation of numbers (with A as 1 and B as 0 and the argument 1 omitted). E.g., 5=`00`, 8=`100`, 12=`1100`, ..., in Wythoff code.
From Petros Hadjicostas, Jan 11 2017: (Start)
a(n) is the number of cyclic sequences consisting of zeros and ones that avoid the pattern 001 (or equivalently, the pattern 110) provided the positions of zeros and ones on a circle are fixed. This can easily be proved by considering that sequence A000071(n+3) is the number of binary zero-one words of length n that avoid the pattern 001 and that a(n) = A000071(n+3) - 2*A000071(n). (From the collection of all zero-one binary sequences that avoid 001 subtract those that start with 1 and end with 00 and those that start with 01 and end with 0.)
For n = 1,2, the number a(n) still gives the number of cyclic sequences consisting of zeros and ones that avoid the pattern 001 (provided the positions of zeros and ones on a circle are fixed) even if we assume that the sequence wraps around itself on the circle. For example, when 01 wraps around itself, it becomes 01010..., and it never contains the pattern 001. (End)
For n >= 3, a(n) is also the number of independent vertex sets and vertex covers in the wheel graph on n+1 nodes. - Eric W. Weisstein, Mar 31 2017

			a(3) = 5 because the following cyclic sequences of length three avoid the pattern 001: 000, 011, 101, 110, 111. - _Petros Hadjicostas_, Jan 11 2017

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

T. D. Noe, Table of n, a(n) for n = 0..500
Nazim Fatès, Biswanath Sethi, and Sukanta Das, On the reversibility of ECAs with fully asynchronous updating: the recurrence point of view, hal-01571847 Preprint, 2017.
Martin Griffiths, On a Matrix Arising from a Family of Iterated Self-Compositions, Journal of Integer Sequences, 18 (2015), #15.11.8.
Fumio Hazama, Spectra of graphs attached to the space of melodies, Discr. Math., 311 (2011), 2368-2383. See Table 5.2.
Martin Herschend and Peter Jorgensen, Classification of higher wide subcategories for higher Auslander algebras of type A, arXiv:2002.01778 [math.RT], 2020.
Dov Jarden, Recurring Sequences, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See p. 97.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Vertex Cover
Eric Weisstein's World of Mathematics, Wheel Graph
Index entries for linear recurrences with constant coefficients, signature (2,0,-1).

Cf. A000032, A000071, A274017.

a001612 n = a001612_list !! n
a001612_list = 3 : 2 : (map (subtract 1) $
   zipWith (+) a001612_list (tail a001612_list))
-- Reinhard Zumkeller, May 26 2013

A001612:=-(-2+3*z**2)/(z-1)/(z**2+z-1); # conjectured by Simon Plouffe in his 1992 dissertation; gives sequence except for the initial 3

Join[{b=3},a=0;Table[c=a+b-1;a=b;b=c,{n,100}]] (* Vladimir Joseph Stephan Orlovsky, Mar 15 2011 *)
Table[Fibonacci[n] + Fibonacci[n - 2] + 1, {n, 20}] (* Eric W. Weisstein, Mar 31 2017 *)
LinearRecurrence[{2, 0, -1}, {3, 2, 4}, 20] (* Eric W. Weisstein, Mar 31 2017 *)
CoefficientList[Series[(3 - 4 x)/(1 - 2 x + x^3), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 21 2017 *)

PARI
```
a(n)=fibonacci(n+1)+fibonacci(n-1)+1
```

G.f.: (3-4*x)/((1-x)*(1-x-x^2)).
a(n) = a(n-1) + a(n-2) - 1.
a(n) = A000032(n) + 1.
a(n) = A000071(n+3) - 2*A000071(n). - Petros Hadjicostas, Jan 11 2017

Additional comments from Michael Somos, Jun 01 2000

A060385 Largest prime factor of n-th Fibonacci number.

Original entry on oeis.org

2, 3, 5, 2, 13, 7, 17, 11, 89, 3, 233, 29, 61, 47, 1597, 19, 113, 41, 421, 199, 28657, 23, 3001, 521, 109, 281, 514229, 61, 2417, 2207, 19801, 3571, 141961, 107, 2221, 9349, 135721, 2161, 59369, 421, 433494437, 307, 109441, 28657, 2971215073, 1103

Offset: 3

Labos Elemer, Apr 03 2001

nonn

For n > 12, Fibonacci(n) is divisible by a primitive prime factor (one not dividing Fibonacci(1), ..., Fibonacci(n-1)). But all primes up to n-2 divide smaller Fibonacci numbers, see A001602, so a(n) >= n-1 for n > 12. This strengthens a more general theorem of Bravo and Luca. - Charles R Greathouse IV, Feb 01 2013

			F(82) = 2789 * 59369 * 370248451, so a(82) = 370248451.

Tyler Busby, Table of n, a(n) for n = 3..1422 (terms 3..1000 from Charles R Greathouse IV, terms 1001..1408 from Amiram Eldar)
U. Alfred, On the form of primitive factors of Fibonacci numbers, Fibonacci Quarterly 1:1 (1963), pp. 43-45.
Jhon J. Bravo and Florian Luca, On the largest prime factor of the k-Fibonacci numbers, arXiv:1210.4101 [math.NT], 2012.
D. E. Daykin and L. A. G. Dresel, Factorization of Fibonacci numbers, Fibonacci Quarterly 8:1 (1970), pp. 23-30.

Cf. A000045, A022307, A001605, A060319, A060320, A051694, A193615.

[Maximum(PrimeDivisors(Fibonacci(n))): n in [3..50]]; // Vincenzo Librandi, Dec 25 2016

Table[First[Last[FactorInteger[Fibonacci[n]]]], {n, 3, 100}] (* Vladimir Joseph Stephan Orlovsky, Feb 03 2012 *)

a(n)=my(f=factor(fibonacci(n))[,1]);f[#f] \\ Charles R Greathouse IV, Feb 01 2013

a(n) >= n - 1 for n > 12, see comments. It is not hard to show that a(n) > 1000 for n > 88. Similarly a(n) > 20641 for n > 120. - Charles R Greathouse IV, Feb 01 2013

A337878 a(n) is the smallest m > 0 such that the n-th prime divides Jacobsthal(m).

Original entry on oeis.org

3, 4, 6, 5, 12, 8, 9, 22, 28, 10, 36, 20, 7, 46, 52, 29, 60, 33, 70, 18, 78, 41, 22, 48, 100, 102, 53, 36, 28, 14, 65, 68, 69, 148, 30, 52, 81, 166, 172, 89, 180, 190, 96, 196, 198, 105, 74, 113, 76, 58, 238, 24, 25, 16, 262, 268, 270, 92, 35, 47, 292, 51

Offset: 2

A.H.M. Smeets, Sep 27 2020

nonn

All positive Jacobsthal numbers are odd, so the index starts at n = 2.
The set of primitive prime factors of J_k is given by {A000040(j) | a(j) = k}.
By definition, a(n) is the multiplicative order of -2 modulo the n-th prime for n > 2. - Jianing Song, Jun 20 2025

			The 4th prime number is 7, and 7 divides 21 which is Jacobsthal(6), so a(4) = 6. The second prime number, 3, divides Jacobsthal(6) as well, but it divides also the smaller Jacobsthal(3), i.e., a(2) = 3.

Jianing Song, Table of n, a(n) for n = 2..10000
Eric Weisstein's World of Mathematics, Primitive Prime Factor

Cf. A000040 (primes), A001045 (Jacobsthal numbers), A001602 (similar for Fibonacci numbers), A105874 (primes having primitive root -2), A129738.
Cf. multiplicative orders of 2..10: A014664, A062117, A082654, A211241, A211242, A211243, A211244, A211245, A002371.
Cf. multiplicative orders of -2..-10: this sequence (if first term 1), A380482, A380531, A380532, A380533, A380540, A380541, A380542, A385222.

m = 300; j = LinearRecurrence[{1, 2}, {3, 5}, m]; s = {}; p = 3; While[(ind = Select[Range[m], Divisible[j[[#]], p] &, 1]) != {}, AppendTo[s, ind[[1]] + 2]; p = NextPrime[p]]; s (* Amiram Eldar, Sep 28 2020 *)

J(n) = (2^n - (-1)^n)/3; \\ A001045
a(n) = {my(k=1, p=prime(n)); while (J(k) % p, k++); k;} \\ Michel Marcus, Sep 29 2020

n = 1
while n < 63:
    n, J0, J1, a = n+1, 3, 1, 3
    p = A000040(n)
    J0 = J0%p
    while J0 != 0:
        J0, J1, a = (J0+2*J1)%p, J0, a+1
    print(n,a)

A000040(n) == 1 (mod a(n)) for n > 2.

A001604 Odd-indexed terms of A124297.

Original entry on oeis.org

11, 31, 151, 911, 5951, 40051, 272611, 1863551, 12760031, 87424711, 599129311, 4106261531, 28144128251, 192901135711, 1322159893351, 9062207833151, 62113268013311, 425730597768451, 2918000731816531, 20000274041790911, 137083916295800111, 939587136717207031, 6440026032054760351

Offset: 0

N. J. A. Sloane

Old name: Related to factors of Fibonacci numbers.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

John Cerkan, Table of n, a(n) for n = 0..1187
Dov Jarden, Recurring Sequences, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See p. 20.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
Index entries for linear recurrences with constant coefficients, signature (11, -33, 33, -11, 1).

Cf. A001603, A124296, A124297.

A001604:=-(11-90*z+173*z**2-90*z**3+11*z**4)/(z-1)/(z**2-3*z+1)/(z**2-7*z+1); # conjectured (correctly) by Simon Plouffe in his 1992 dissertation

5 #^2 + 5 # + 1 &@ Fibonacci@ # & /@ Range[1, 45, 2] (* Michael De Vlieger, Apr 03 2017 *)

G.f.: -(11-90*x+173*x^2-90*x^3+11*x^4)/((x-1)*(x^2-3*x+1)*(x^2-7*x+1)). [After Simon Plouffe]

a(n) = (5+sqrt(5))/2*((3+sqrt(5))/2)^n+(5-sqrt(5))/2*((3-sqrt(5))/2)^n+(3+sqrt(5))/2*((7+3*sqrt(5))/2)^n+(3-sqrt(5))/2*((7-3*sqrt(5))/2)^n+3. [Tim Monahan, Aug 15 2011]

Entry revised by Michel Marcus and N. J. A. Sloane, Jun 06 2015

A178763 Product of primitive prime factors of Fibonacci(n).

Original entry on oeis.org

1, 1, 2, 3, 5, 1, 13, 7, 17, 11, 89, 1, 233, 29, 61, 47, 1597, 19, 4181, 41, 421, 199, 28657, 23, 3001, 521, 5777, 281, 514229, 31, 1346269, 2207, 19801, 3571, 141961, 107, 24157817, 9349, 135721, 2161, 165580141, 211, 433494437, 13201, 109441, 64079

Offset: 1

T. D. Noe, Jun 10 2010

nonn

Same as A001578 for the first 18 terms.

Let b(n) be the greatest divisor of Fibonacci(n) that is coprime to Fibonacci(m) for all positive integers m < n, then a(n) = b(n) for all n, provided that no Wall-Sun-Sun prime exists. Otherwise, if p is a Wall-Sun-Sun prime and A001177(p) = k (then A001177(p^2) = k), then p^2 divides b(k), but by definition a(k) is squarefree. - Jianing Song, Jul 02 2019

T. D. Noe, Table of n, a(n) for n = 1..1000
Dov Jarden, Recurring Sequences, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy] See pp. 60-64 for a table of the first 385 terms.
Florian Luca, Carl Pomerance, and Stephen Wagner, Fibonacci Integers (preprint)

Cf. A061446, A086597, A152012 (Indices of prime terms).

a(n)=my(d=divisors(n), f=fibonacci(n), t); t=lcm(apply(fibonacci,d[1..#d-1])); while((t=gcd(t,f))>1, f/=t); f \\ Charles R Greathouse IV, Nov 30 2016

a(n) = A061446(n) / A178764(n).

a(n) = A061446(n) / gcd(A061446(n), n) if n != 5, 6, provided that no Wall-Sun-Sun prime exists. - Jianing Song, Jul 02 2019

A065069 Numbers n such that Fibonacci(n) is not squarefree, but for all proper divisors k of n, Fibonacci(k) is squarefree.

Original entry on oeis.org

6, 25, 56, 91, 110, 153, 406, 703, 752, 820, 915, 979, 1431, 1892, 2147, 2701, 2943, 3029, 3422, 4378, 4556, 4753, 4970, 5513, 6394, 7868, 8841, 9453, 10712, 12403, 13508, 13546, 15051, 16256, 17030, 17267, 18023, 18721, 19503, 20827, 21206

Offset: 1

Len Smiley, Nov 07 2001

nonn

These are first primitive indices m for which Fib(m) is squareful. Note that Fib(km) is divisible by Fib(m).
This sequence is closely related to A001602(n), which gives the index of the smallest Fibonacci number divisible by prime(n). It can be shown that the index of the first Fibonacci number divisible by prime(n)^2 is A001602(n)*prime(n). This sequence is the collection of numbers A001602(n)*prime(n) with multiples removed. For example, A001602(2)*prime(2) = 12, but all multiples of 12 will generated by 6, the first number in this sequence. The Mathematica code assumes that Fibonacci numbers do not have any square primitive prime factors -- an assumption whose truth is an open question. - T. D. Noe, Jul 24 2003
These are the primitive elements of A037917. - Charles R Greathouse IV, Feb 02 2014
Terms after a(12) are conjectures until the factorizations of F(1271), F(1273), etc. are completed. - Charles R Greathouse IV, Feb 02 2014
Three more factorizations are needed to get the next term: F(1423), F(1427), and F(1429). If these are each squarefree, a(13) = 1431. - Charles R Greathouse IV, Dec 09 2022

			a(1) = 6 because 2^2 divides Fibonacci(6) but no smaller Fibonacci number.

Hisanori Mishima, Factorizations of Fibonacci numbers: n=1..100, n=101..200, n=201..300, n=301..400, n=401..480.
Blair Kelly, Fibonacci and Lucas Factorizations

Cf. A037917 (all indices <= 240 for which Fib(m) is squareful).

Cf. A065106, A001602, A013929 (not squarefree).

<< NumberTheory`NumberTheoryFunctions`; a = {}; l = 0; Do[m = n; If[k = 1; While[k < l + 1 && !IntegerQ[ n/ a[[k]]], k++ ]; k > l, If[ !SquareFreeQ[ Fibonacci[n]], a = Append[a, n]; l++; Print[n]]], {n, 1, 480} ]
nLimit=50000; i=3; pMax=1; iMax=1; While[p=Transpose[FactorInteger[Fibonacci[i]]][[1, -1]]; i*ppMax, pMax=p; iMax=i]; i++ ]; nMax=PrimePi[pMax]; fs={}; Do[p=Prime[n]; k=1; found=False; While[found=(Mod[Fibonacci[k], p]==0); !found&&k*p0, j=i+1; While[j<=Length[fs], If[Mod[fs[[j]], n]==0, fs[[j]]=0]; j++ ]]; i++ ]; Select[fs, #>0&&#

PARI
```
is_A065069(n)=!fordiv(n,k,k>1 && k1 \\
```

One more term from Robert G. Wilson v, Nov 08 2001

More terms from T. D. Noe, Jul 24 2003

A079346 Primes p such that F(p-(p/5)) is the first Fibonacci number that p divides.

Original entry on oeis.org

2, 3, 5, 7, 11, 19, 23, 31, 43, 59, 67, 71, 79, 83, 103, 127, 131, 163, 167, 179, 191, 223, 227, 239, 251, 271, 283, 311, 359, 367, 379, 383, 419, 431, 439, 443, 463, 467, 479, 487, 491, 499, 503, 523, 547, 571, 587, 599, 607, 631, 643, 647, 659, 683, 719, 727, 739, 751, 787, 823, 827

Offset: 1

Jon Perry, Jan 04 2003

nonn

The n-th prime p is in this sequence iff A001602(n) = p-(5/p) (that is the maximum possible value of A001602(n)).

			7 belongs to this sequence since (7/5) = -1, F(8) = 21 and 7 does not divide F(1) to F(7).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Union of A000057, A106535 and {5}.

Cf. A001602, A079347, A079348, A079349.

forprime (p=2,500, wss=p-kronecker(5,p); for(n=1, wss, if( fibonacci(n)%p==0, if( n==wss, print1(p","), break) ) ))

Corrected and edited by Max Alekseyev, Nov 23 2007

A135952 Prime factors of composite Fibonacci numbers with prime indices (cf. A050937).

Original entry on oeis.org

37, 73, 113, 149, 157, 193, 269, 277, 313, 353, 389, 397, 457, 557, 613, 673, 677, 733, 757, 877, 953, 977, 997, 1069, 1093, 1153, 1213, 1237, 1453, 1657, 1753, 1873, 1877, 1933, 1949, 1993, 2017, 2137, 2221, 2237, 2309, 2333, 2417, 2473, 2557, 2593, 2749, 2777, 2789, 2797, 2857, 2909, 2917, 3217, 3253, 3313, 3517, 3557, 3733, 4013, 4057, 4177, 4273, 4349, 4357, 4513, 4637, 4733, 4909, 4933

Offset: 1

Artur Jasinski, Dec 08 2007

nonn

All numbers in this sequence are congruent to 1 mod 4. - Max Alekseyev.
If Fibonacci(n) is divisible by a prime p of the form 4k+3 then n is even. To prove this statement it is enough to show that (1+sqrt(5))/(1-sqrt(5)) is never a square modulo such p (which is a straightforward exercise).
The n-th prime p is an element of this sequence iff A001602(n) is prime and A051694(n)=A000045(A001602(n))>p. - Max Alekseyev

Hans Havermann, Table of n, a(n) for n = 1..5000

Cf. A000045, A001605, A050937, A075737, A090819, A134787, A134851, A134852.

a = {}; k = {}; Do[If[ !PrimeQ[Fibonacci[Prime[n]]], s = FactorInteger[Fibonacci[Prime[n]]]; c = Length[s]; Do[AppendTo[k, s[[m]][[1]]], {m, 1, c}]], {n, 2, 60}]; Union[k]

Edited, corrected and extended by Max Alekseyev, Dec 12 2007

A233281 Numbers n such that the least Fibonacci number F_k which is a multiple of n has a prime index, i.e., k is in A000040.

Original entry on oeis.org

2, 5, 13, 37, 73, 89, 113, 149, 157, 193, 233, 269, 277, 313, 353, 389, 397, 457, 557, 613, 673, 677, 733, 757, 877, 953, 977, 997, 1069, 1093, 1153, 1213, 1237, 1453, 1597, 1657, 1753, 1873, 1877, 1933, 1949, 1993, 2017, 2137, 2221, 2237, 2309, 2333, 2417, 2473

Offset: 1

Antti Karttunen, Dec 13 2013

nonn

Numbers n such that A001177(n) is prime.
Each natural number n belongs to this sequence if the smallest Fibonacci number which it divides is a term of A030426. - Jon E. Schoenfield, Feb 28 2014
A092395 gives all the primes in this sequence (cf. Wikipedia-link), and the first composite occurs as the 69th term, where a(69)=4181 while A092395(69)=4273. After 4181 (= 37*113 = F_19), the next term missing from A092395 is a(148)=10877 (= 73*149. A001177(10877) = 37, F_37 = 24157817 = 2221*10877). Both of these numbers (4181 and 10877) occur in various lists of Fibonacci-related pseudoprimes. Sequence A238082 gives all composites occurring in this sequence.
If n is in this sequence then all divisors d > 1 of n are in this sequence. - Charles R Greathouse IV, Feb 04 2014
Composite members begin 4181, 10877, 75077, 162133, 330929, .... - Charles R Greathouse IV, Mar 07 2014

Antti Karttunen and Charles R Greathouse IV, Table of n, a(n) for n = 1..2000 (first 157 terms from Karttunen)
Wikipedia, Fibonacci prime, section: Divisibility of Fibonacci numbers

Disjoint union of A092395 and A238082. The first 68 terms are identical with A092395, after which follows the first case of the latter sequence, with a(69) = A238082(1) = 4181.

Cf. A000045, A001177, A001602, A030426, A051694, A060442, A086597, A233282.

a233281 n = a233281_list !! (n-1)
a233281_list = filter ((== 1) . a010051 . a001177) [1..]
-- Reinhard Zumkeller, Apr 04 2014

is(n)=my(k); while(fibonacci(k++)%n, ); isprime(k) \\ Charles R Greathouse IV, Feb 04 2014

entry(p)=my(k=1);while(fibonacci(k++)%p,);k;
is(n)={
    if(n%2==0,return(n==2));
    if(n<13, return(n==5));
    my(f=factor(n),p,F);
    if(f[1,2]>1 && f[1,1]<1e14,return(0));
    p=entry(f[1,1]);
    F=fibonacci(p);
    if(f[1,2]>1 && F%f[1,1]^f[1,2],return(0));
    if(!isprime(p), return(0));
    for(i=2,#f~,
        if(F%f[i,1]^f[i,2],return(0))
    );
    1
}; \\ Charles R Greathouse IV, Feb 04 2014

A010051(A001177(a(n))) = 1. - Reinhard Zumkeller, Apr 04 2014

cp's OEIS Frontend

A051694 Smallest Fibonacci number that is divisible by n-th prime.

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A001612 a(n) = a(n-1) + a(n-2) - 1 for n > 1, a(0)=3, a(1)=2.

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A060385 Largest prime factor of n-th Fibonacci number.

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A337878 a(n) is the smallest m > 0 such that the n-th prime divides Jacobsthal(m).

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A001604 Odd-indexed terms of A124297.

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Maple

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A178763 Product of primitive prime factors of Fibonacci(n).

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