A091982 Nonprimes k such that Mod(k,4) == 1 and denominator(Fibonacci((k-1)/4)/k) = 1.

1, 4181, 6721, 13201, 34561, 51841, 64681, 90061, 96049, 97921, 163081, 186961, 197209, 268801, 283361, 302101, 330929, 399001, 489601, 520801, 636641, 655201, 920577, 999941, 1034881, 1072513, 1081649, 1084201, 1106561, 1317121, 1346269, 1392169, 1533601

Offset

1,2

Links

Giovanni Resta, Table of n, a(n) for n = 1..2500

Mathematica

Select[Range[1, 10^6, 4], And[! PrimeQ@ #, Denominator[Fibonacci[(# - 1)/4]/#] == 1] &] (* Michael De Vlieger, May 07 2017 *)

Prog

(Python)
from itertools import islice, count
from sympy import isprime
def A091982_gen(): # generator of terms
    def fibonacci_mod(n, m): # fibonacci(n) mod m
        a, b, c, d, a2, b2, c2, d2 = 1, 1, 1, 0, 1, 0, 0, 1
        for x in bin(n)[2:]:
            e, f = b2*c2%m, a2+d2
            a2, b2, c2, d2 = (pow(a2, 2, m)+e)%m, b2*f%m, c2*f%m, (pow(d2, 2, m)+e)%m
            if x=='1':
                a2, b2, c2, d2 = (a2*a+b2*c)%m, (a2*b+b2*d)%m, (c2*a+d2*c)%m, (c2*b+d2*d)%m
        return c2
    for m in count(1, 4):
        if not isprime(m) and fibonacci_mod(m-1>>2, m)==0:
            yield m
A091982_list = list(islice(A091982_gen(), 20)) # Chai Wah Wu, Jul 03 2026

Crossrefs

For primes see A047272.

Sequence in context: A093372 A212424 A319168 * A238082 A072322 A045728

Adjacent sequences: A091979 A091980 A091981 * A091983 A091984 A091985

Keyword

nonn,easy

Author

Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 17 2004

Extensions

a(16)-a(33) from Giovanni Resta, May 06 2017

Status

approved