A279795
Numbers n such that F(n) and F(n-2) are both prime where F(n) = A000045(n).
Original entry on oeis.org
5, 7, 13, 433, 571
Offset: 1
13 is a term because Fibonacci(13) = 233 and Fibonacci(11) = 89 are both prime.
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Select[Range[10^4], Times @@ Boole@ Map[PrimeQ@ Fibonacci@ # &, {#, # - 2}] > 0 &] (* Michael De Vlieger, Jan 21 2017 *)
Flatten[Position[Partition[Fibonacci[Range[580]],3,1],?(AllTrue[ {#[[1]],#[[3]]},PrimeQ]&),1,Heads->False]]+2 (* _Harvey P. Dale, Oct 01 2021 *)
-
isok(n) = isprime(fibonacci(n)) && isprime(fibonacci(n-2)); \\ Michel Marcus, Jan 14 2017
A073340
Fibonacci prime pairs: the indices of each pair differ by two and the relevant Fibonacci numbers are both prime.
Original entry on oeis.org
3, 5, 5, 7, 11, 13, 431, 433, 569, 571
Offset: 1
The 431st Fibonacci number and the 433rd Fibonacci number are both prime and their indices differ by 2.
- David Wells, The Penguin Dictionary of Curious and Interesting Numbers, Penguin Books, Rev. ed. 1997, p. 46.
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Flatten[Select[Partition[Select[Range[3000], PrimeQ[Fibonacci[ # ]]&], 2, 1], #[[2]] - #[[1]] == 2 &]]
-
from sympy import isprime
def afind(limit):
i, fnm2, fnm1 = 1, 1, 1
while i < limit:
if isprime(fnm2) and isprime(fnm2 + fnm1):
print(i, i+2, sep=", ", end=", ")
i, fnm2, fnm1 = i+1, fnm1, fnm2 + fnm1
afind(600) # Michael S. Branicky, Mar 05 2021
A297624
Numbers k such that Fibonacci(2*k+1) and Fibonacci(2*k-1) are prime.
Original entry on oeis.org
2, 3, 6, 216, 285
Offset: 1
2 is in the sequence because F(3)=2 and F(5)=5 are prime.
6 is in the sequence because F(11)=89 and F(13)=233 are prime.
-
o := [];; for k in [1..500] do if IsPrime(Fibonacci(2*k+1)) and IsPrime(Fibonacci(2*k-1)) then Add(o,k); fi; od; A297624 := o; # Muniru A Asiru, Jan 25 2018
-
[n: n in [0..700] | IsPrime(Fibonacci(2*n+1)) and IsPrime(Fibonacci(2*n-1))];
-
with(combinat, fibonacci): select(k -> isprime(fibonacci(2*k+1)) and isprime(fibonacci(2*k-1)), [$1..500]); # Muniru A Asiru, Jan 25 2018
-
Select[Range[0, 3000], PrimeQ[Fibonacci[2 # + 1]] && PrimeQ[Fibonacci[2 # - 1]] &]
-
isok(n) = isprime(fibonacci(2*n-1)) && isprime(fibonacci(2*n+1)); \\ Michel Marcus, Jan 08 2018
-
from sympy import isprime
A297624_list, k, a, b, c, aflag = [], 1, 1, 1, 2, False
while k < 1000:
cflag = isprime(c)
if aflag and cflag:
A297624_list.append(k)
k, a, b, c, aflag = k + 1, c, b + c, b + 2*c, cflag # Chai Wah Wu, Jan 23 2018
A328381
Lesser of twin primes pair p, such that F(p) and F(p+2) have the same number of prime factors, where F(n) is the n-th Fibonacci number.
Original entry on oeis.org
3, 5, 11, 59, 71, 107, 179, 191, 311, 431, 569, 599, 827, 881
Offset: 1
3 is in the sequence since 3 and 5 are twin primes, and F(3) = 2 and F(5) = 5 are both primes, thus having the same number of prime factors.
71 is in the sequence since 71 and 73 are twin primes, and F(71) and F(73) both have 2 prime factors.
-
s={}; Do[If[PrimeQ[n] && PrimeQ[n+2] && PrimeOmega[Fibonacci[n]] == PrimeOmega[ Fibonacci[n+2]], AppendTo[s, n]], {n, 1, 200}]; s
A350707
Numbers m such that all prime factors of m^2+1 are Fibonacci numbers.
Original entry on oeis.org
0, 1, 2, 3, 5, 7, 8, 18, 34, 57, 144, 239, 322, 610, 1134903170
Offset: 1
57 is in the sequence because 57^2+1 = 2*5^3*13 and 2, 5 and 13 are Fibonacci numbers;
1134903170 = Fibonacci(45) is in the sequence because 1134903170^2+1 = 433494437*2971215073 = Fibonacci(43)*Fibonacci(47).
-
with(numtheory):
A005478:={2, 3, 5, 13, 89, 233, 1597, 28657, 514229, 433494437, 2971215073, 99194853094755497,1066340417491710595814572169, 19134702400093278081449423917}:
for n from 0 to 11000 do:
y:=factorset(n^2+1):n0:=nops(y):
if A005478 intersect y = y
then
print(n):
else
fi:
od:
-
isfib(n) = my(k=n^2); k+=(k+1)<<2; issquare(k) || (n>0 && issquare(k-8));
isok(m) = my(f=factor(m^2+1)); for (i=1, #f~, if (!isfib(f[i,1]), return(0))); return(1); \\ Michel Marcus, Mar 29 2022
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