A051694 -id:A051694 - cp's OEIS frontend

A060321 Erroneous version of A051694.

2, 3, 5, 21, 55, 377, 34, 2584, 46368, 377, 832040, 4181, 6763, 987, 196418

Offset: 1

dead

A001602 Fibonacci entry points: a(n) = smallest m > 0 such that the n-th prime divides Fibonacci(m).

3, 4, 5, 8, 10, 7, 9, 18, 24, 14, 30, 19, 20, 44, 16, 27, 58, 15, 68, 70, 37, 78, 84, 11, 49, 50, 104, 36, 27, 19, 128, 130, 69, 46, 37, 50, 79, 164, 168, 87, 178, 90, 190, 97, 99, 22, 42, 224, 228, 114, 13, 238, 120, 250, 129, 88, 67, 270, 139, 28, 284, 147, 44, 310

Offset: 1

N. J. A. Sloane

"[a(n)] is called by Lucas the rank of apparition of p and we know it is a divisor of, or equal to prime(n)-1 or prime(n)+1" - Vajda, p. 84. (Note that a(3)=5. This is the only exception.) - Chris K. Caldwell, Nov 03 2008
Every number except 1, 2, 6 and 12 eventually occurs in this sequence. See also A086597(n), the number of primitive prime factors of Fibonacci(n). - T. D. Noe, Jun 13 2008
For each prime p we have an infinite sequence of integers, F(i*a(n))/p, i=1,2,... See also A236479. For primes p >= 3 and exponents j >= 2, with k = a(n) and p = p(n), it appears that F(k*i*p^(j-1))/p^j is an integer, for i >= 0. For p = 2, F(k*i*p^(j-1))/p^(j+1) = integer. - Richard R. Forberg, Jan 26-29 2014 [Comments revised by N. J. A. Sloane, Sep 24 2015]
Let p=prime(n). a(n) is also a divisor of (p-1)/2 (if p mod 5 == 1 or 4) or (p+1)/2 (if p mod 5 == 2 or 3) if and only if p mod 4 = 1. - Seiichi Azuma, Jul 29 2014

			The 5th prime is 11 and 11 first divides Fib(10)=55, so a(5) = 10.

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).
S. Vajda, Fibonacci and Lucas numbers and the Golden Section, Ellis Horwood Ltd., Chichester, 1989.

T. D. Noe, Table of n, a(n) for n = 1..10000
U. Alfred, M. Wunderlich, Tables of Fibonacci Entry Points, Part I, (1965).
Miho Aoki and Yuho Sakai, On Equivalence Classes of Generalized Fibonacci Sequences, JIS vol 19 (2016) # 16.2.6
B. Avila, T. Khovanova, Free Fibonacci SequencesJ. Int. Seq. 17 (2014) # 14.8.5.
Alfred Brousseau, Fibonacci and Related Number Theoretic Tables, Fibonacci Association, San Jose, CA, 1972. See p. 25.
Paul Cubre and Jeremy Rouse, Divisibility properties of the Fibonacci entry point, arXiv:1212.6221 [math.NT], 2012.
D. E. Daykin and L. A. G. Dresel, Factorization of Fibonacci Numbers part 2, Fibonacci Quarterly, vol 8 (1970), pages 23 - 30 and 82.
Ramon Glez-Regueral, An entry-point algorithm for high-speed factorization, Thirteenth Internat. Conf. Fibonacci Numbers Applications, Patras, Greece, 2008.
R. K. Guy, The Second Strong Law of Small Numbers, Math. Mag, 63 (1990), no. 1, 3-20. [Annotated scanned copy]
Dov Jarden, Recurring Sequences, Riveon Lematematika, Jerusalem, 1966. [Annotated scanned copy, pp. 2-3 missing] See p. 7.
D. Lind et al., Tables of Fibonacci entry points, part 2, reviewed in, Math. Comp., 20 (1966), 618-619.
Patrick McKinley, Table of a(n) for n=1..678921
Daniel Yaqubi, Amirali Fatehizadeh, Some results on average of Fibonacci and Lucas sequences, arXiv:2001.11839 [math.CO], 2020.

Cf. A051694, A001177, A086597, A194363 (entries Lucas).

import Data.List (findIndex)
import Data.Maybe (fromJust)
a001602 n = (+ 1) $ fromJust $
            findIndex ((== 0) . (`mod` a000040 n)) $ tail a000045_list
-- Reinhard Zumkeller, Apr 08 2012

A001602 := proc(n)
    local i,p;
    p := ithprime(n);
    for i from 1 do
        if modp(combinat[fibonacci](i),p) = 0 then
            return i;
        end if;
    end do:
end proc: # R. J. Mathar, Oct 31 2015

Table[k=1;While[!Divisible[Fibonacci[k],Prime[n]],k++];k,{n,70}] (* Harvey P. Dale, Feb 15 2012 *)
(* a fast, but more complicated method *) MatrixPowerMod[mat_, n_, m_Integer] := Mod[Fold[Mod[If[#2 == 1, #1.#1.mat, #1.#1], m] &, mat, Rest[IntegerDigits[n, 2]]], m]; FibMatrix[n_Integer, m_Integer] := MatrixPowerMod[{{0, 1}, {1, 1}}, n, m]; FibEntryPointPrime[p_Integer] := Module[{n, d, k}, If[PrimeQ[p], n = p - JacobiSymbol[p, 5]; d = Divisors[n]; k = 1; While[FibMatrix[d[[k]], p][[1, 2]] > 0, k++]; d[[k]]]]; SetAttributes[FibEntryPointPrime, Listable]; FibEntryPointPrime[Prime[Range[10000]]] (* T. D. Noe, Jan 03 2013 *)
With[{nn=70,t=Table[{n,Fibonacci[n]},{n,500}]},Transpose[ Flatten[ Table[ Select[t,Divisible[#[[2]],Prime[i]]&,1],{i,nn}],1]][[1]]] (* Harvey P. Dale, May 31 2014 *)

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

do(p)=my(k=p+[0,-1,1,1,-1][p%5+1],f=factor(k));for(i=1,#f[,1],for(j=1,f[i,2],if((Mod([1,1;1,0],p)^(k/f[i,1]))[1,2], break); k/=f[i,1])); k
a(n)=do(prime(n))
apply(do, primes(100)) \\ Charles R Greathouse IV, Jan 03 2013

from sympy.ntheory.generate import prime
def A001602(n):
    a, b, i, p = 0, 1, 1, prime(n)
    while b % p:
        a, b, i = b, (a+b) % p, i+1
    return i # Chai Wah Wu, Nov 03 2015, revised Apr 04 2016.

a(n) = A001177(prime(n)).

a(n) <= prime(n) + 1. - Charles R Greathouse IV, Jan 02 2013

More terms from Jud McCranie

A060384 Number of decimal digits in n-th Fibonacci number.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18

Offset: 0

Labos Elemer, Apr 03 2001

Harry J. Smith, Table of n, a(n) for n = 0..10000

Cf. A000045, A022307, A001605, A060319, A060320, A051694, A050815.

Cf. A261585.

a060384 = a055642 . a000045  -- Reinhard Zumkeller, Mar 09 2013

with(combinat): a:=n->nops(convert(fibonacci(n),base,10)): 1,seq(a(n),n=1..100); # Emeric Deutsch, May 19 2007

Table[IntegerLength@ Fibonacci@ n, {n, 0, 84}] /. 0 -> 1 (* or *)
Table[Floor[n Log10@ GoldenRatio - Log10@ 5/2] + 1, {n, 0, 84}] /. 0 -> 1 (* Michael De Vlieger, Jul 04 2016 *)

print1("1, 1, "); gold=(1+sqrt(5))/2; for(n=2,100,print1(floor((n*log(gold)-log(5)/2)/log(10))+1", ")) \\ Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007

a(n) = #Str(fibonacci(n)); \\ Michel Marcus, Jul 04 2016

a(n) = floor(n*log(tau)/log(10)) +0 or +1 where tau is the golden ratio. - Benoit Cloitre, Oct 29 2002. [Corrected by Hans J. H. Tuenter, Jul 07 2025].
a(n) = floor(n*log_10(gold) - log_10(5)/2) + 1 for n >= 2, where gold is (1+sqrt(5))/2. - Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007
a(n) = A055642(A000045(n)). - Reinhard Zumkeller, Mar 09 2013

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), May 01 2007

A060320 Index of smallest Fibonacci number with exactly n distinct prime factors.

Original entry on oeis.org

1, 3, 8, 15, 20, 30, 40, 70, 60, 80, 90, 140, 176, 120, 168, 180, 324, 252, 240, 378, 450, 432, 552, 360, 420, 690, 504, 880, 630, 600, 756, 720, 900, 792, 840, 1296, 1050, 1350, 1140, 1080, 1200, 1824, 1260, 1512, 1320, 1560, 1680

Offset: 0

Labos Elemer, Mar 28 2001

From Jon E. Schoenfield, Dec 28 2016: (Start)
 Note that the presence of incompletely factored Fibonacci numbers with indices as low as 1301 does not prevent the drawing of conclusions such as "a(44) = 1320" with certainly. Using F(1301) as an example, the compact table of Fibonacci results at the Kelly site indicates that F(1301) = p*q*r*c where p=6400921, q=14225131397, r=100794731109596201, and c is a 238-digit unfactored composite number. The complete factorization of every Fibonacci number up to F(1000) is explicitly given elsewhere on the site, and those results allow quick verification that a(n) <= 900 for all n in [0..34], so 1301 cannot be a term unless F(1301) has at least 35 distinct prime factors, which would require c to have at least 32 distinct prime factors, at least one of which would have to be less than ceiling(c^(1/32)) = 26570323, but trial division of c by every prime less than 26570323 shows that c has no prime factors that small. Thus, while A022307(1301) is unknown, it is certain that 1301 is not a term in this sequence. Similarly, making use of known factors, it can be proved that F(n) cannot have 44 or more distinct prime factors for any n < 1320, so since F(1320) has exactly 44 distinct prime factors, it is established that a(44) = 1320. (End)
a(47) >= 2835, a(48..68) = (2040, 1800, 2736, 2730, 1890, 1980, 2520, 2280, 2100, 2160, 2640, 3300, 3060, 3150, 2520, 3120, 3696, 3240, 3990, 3360, 3420), a(69) >= 4400, a(75) = 4320, a(77) = 4200, a(79) = 3780. - Max Alekseyev, Feb 03 2025

			n=9: F(80) = 23416728348467685 = 3 * 5 * 7 * 11 * 41 * 47 * 1601 * 2161 * 3041.
n=25: F(690) = 2^3 * 5 * 11 * 31 * 61 * 137 * 139 * 461 * 691 * 829 * 1151 * 1381 * 4831 * 5981 * 18077 * 28657 * 186301 * 324301 * 686551 * 1485571 * 4641631 * 117169733521 * 2441738887963981 * 3490125311294161 * 25013864044961447973152814604981 is the smallest Fibonacci number with exactly 25 distinct prime factors.

Ron Knott, Fibonacci numbers with tables of F(0)-F(500)
Hisanori Mishima, Fibonacci numbers (n = 1 to 100, n = 101 to 200, n = 201 to 300, n = 301 to 400, n = 401 to 480).

Cf. A001605, A005478, A022307, A051694, A060319.

Row n=1 of A303217.

First /@ SortBy[#, Last] &@ Map[First@ # &, Values@ GroupBy[#, Last]] &@ Table[{n - Boole[n == 2], #, PrimeNu@ #} &@ Fibonacci@ n, {n, 2, 300}] (* Michael De Vlieger, Feb 18 2017, Version 10 *)
Module[{ff=Table[{n,PrimeNu[Fibonacci[n]]},{n,1400}]},Table[ SelectFirst[ ff,#[[2]]==k&],{k,0,40}]][[All,1]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 28 2018 *)

my(o=[],s); print1(1); for(n=1,20, s=0; until( o[s]==n, #o

a(n) = min (k : A022307(k) = n).

Corrected by Shyam Sunder Gupta, Jul 20 2002
Edited by M. F. Hasler, Nov 01 2012
a(35)-a(40), a(42), a(44) computed based on Kelly's data in A022307 by Jon E. Schoenfield, Dec 28 2016
a(41), a(43), a(45)-a(46) from Max Alekseyev, Feb 03 2025

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

A060383 a(1) = a(2) = 1; for n >2, a(n) = smallest prime factor of n-th Fibonacci number.

Original entry on oeis.org

1, 1, 2, 3, 5, 2, 13, 3, 2, 5, 89, 2, 233, 13, 2, 3, 1597, 2, 37, 3, 2, 89, 28657, 2, 5, 233, 2, 3, 514229, 2, 557, 3, 2, 1597, 5, 2, 73, 37, 2, 3, 2789, 2, 433494437, 3, 2, 139, 2971215073, 2, 13, 5, 2, 3, 953, 2, 5, 3, 2, 59, 353, 2, 4513, 557, 2, 3, 5, 2, 269, 3, 2, 5

Offset: 1

Labos Elemer, Apr 03 2001

nonn

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

Tyler Busby, Table of n, a(n) for n = 1..1452 (terms 1..1000 from Alois P. Heinz, derived from Kelly's data, terms 1001..1408 from Amiram Eldar)
Blair Kelly, Fibonacci and Lucas Factorizations

Cf. A000045, A022307, A001605, A060319, A060320, A051694, A139044.

[1,1] cat [Minimum(PrimeDivisors(Fibonacci(n))): n in [3..70]]; // Vincenzo Librandi, Dec 25 2016

f[n_] := (FactorInteger@ Fibonacci@ n)[[1,1]]; Array[f, 70] (* Robert G. Wilson v, Jul 07 2007 *)

a(n) = if ((f=fibonacci(n))==1, 1, factor(f)[1,1]); \\ Michel Marcus, Nov 15 2014

a(n) = A020639(A000045(n)). - Michel Marcus, Nov 15 2014

Better definition from Omar E. Pol, Apr 25 2008

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

A262708 a(n) = p-(p/5) where p = prime(n) and (p/5) is a Legendre symbol.

Original entry on oeis.org

8, 10, 14, 18, 18, 24, 28, 30, 38, 40, 44, 48, 54, 58, 60, 68, 70, 74, 78, 84, 88, 98, 100, 104, 108, 108, 114, 128, 130, 138, 138, 148, 150, 158, 164, 168, 174, 178, 180, 190, 194, 198, 198, 210, 224, 228, 228, 234, 238, 240, 250, 258, 264, 268, 270, 278, 280

Offset: 4

Shane Findley, Sep 27 2015

nonn

The sequence lists Fibonacci indices q that are conjectured to produce Fibonacci numbers divisible by p^2, where p is a Fibonacci-Wieferich prime.

			For n=4, prime(4)=7, and a(4)=8.

Paulo Ribenboim, My Numbers, My Friends, Springer-Verlag, 2000.
Steven Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Dover. (See p. 73.)

U. Alfred, On the form of primitive factors of Fibonacci numbers, Volume 1, Fibonacci Quarterly, vol 1 (1963), page 1.
Andreas-Stephan Elsenhans, The Fibonacci sequence modulo p^2., pages 1-6.
Shane Findley, Discussion of Sequence A262708.
Richard J. McIntosh and Eric L. Roettger, A search for Fibonacci-Wieferich and Wolstenholme primes, Mathematics of Computation, vol 76 (260), Oct 2007.
John Vinson, The Relation of the Period Modulo m to the Rank of Apparition of m in the Fibonacci Sequence, Fibonacci Quarterly, vol 1 (1963), pages 37-45.

Cf. A001602, A051694.

Table[Prime@ n - JacobiSymbol[Prime@ n, 5], {n, 4, 60}] (* Michael De Vlieger, Oct 04 2015 *)

lista(nn)=forprime(p=3, nn, print1(p-kronecker(p, 5), ", ");); \\ Michel Marcus, Sep 29 2015

Edited by N. J. A. Sloane, Sep 29 2015

Edited by Jon E. Schoenfield, Oct 09 2015

A111331 Prime Fibonacci numbers whose digits in base 10 sum up to a prime.

Original entry on oeis.org

2, 3, 5, 89, 514229, 433494437, 2971215073, 3061719992484545030554313848083717208111285432353738497131674799321571238149015933442805665949

Offset: 1

Stefan Steinerberger, Nov 05 2005

Fibonacci(104911) is the next (probable) prime whose digits sum to a prime. Thus the next term would be 21925 digits long. - Hans Havermann, Nov 06 2005

			514229 is a prime Fibonacci number and the sum of the digits 5 + 1 + 4 + 2 + 2 + 9 = 23 is also a prime.

Cf. A065398, A051694, A051694, A067515.

Select[Fibonacci[Range[1000]],PrimeQ[#]&&PrimeQ[Total[IntegerDigits[#]]]&] (* James C. McMahon, May 31 2024 *)

cp's OEIS Frontend

A060321 Erroneous version of A051694.

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A001602 Fibonacci entry points: a(n) = smallest m > 0 such that the n-th prime divides Fibonacci(m).

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A060384 Number of decimal digits in n-th Fibonacci number.

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A060320 Index of smallest Fibonacci number with exactly n distinct prime factors.

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A060385 Largest prime factor of n-th Fibonacci number.

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A060383 a(1) = a(2) = 1; for n >2, a(n) = smallest prime factor of n-th Fibonacci number.

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

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