OFFSET
1,1
COMMENTS
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
LINKS
Antti Karttunen and Charles R Greathouse IV, Table of n, a(n) for n = 1..2000 (first 157 terms from Karttunen)
FORMULA
PROG
(Scheme, with Antti Karttunen's IntSeq-library)
(PARI) is(n)=my(k); while(fibonacci(k++)%n, ); isprime(k) \\ Charles R Greathouse IV, Feb 04 2014
(PARI) 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
(Haskell)
a233281 n = a233281_list !! (n-1)
a233281_list = filter ((== 1) . a010051 . a001177) [1..]
-- Reinhard Zumkeller, Apr 04 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Dec 13 2013
STATUS
approved