A094400 Odd n dividing Fibonacci(n)-1 but neither Fibonacci(n-1) nor Fibonacci(n+1).

7743, 27071, 54839, 72831, 217257, 388367, 417601, 575599, 670879, 691447, 701569, 809999, 850541, 881011, 1274897, 1365407, 1383249, 1464449, 1504097, 1653751, 1922817, 2106017, 2276351, 2385811, 2474047, 2556553, 2628879, 2697899, 2804543, 3017729, 3352049

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..559 (terms < 4*10^9)

Mathematica

Select[Range[50000], OddQ[ # ] && Mod[Fibonacci[ # ] - 1, # ] == 0 && ! Mod[Fibonacci[ # - 1], # ] == 0 && ! Mod[Fibonacci[ # + 1], # ] == 0 &]

Prog

(Python)
from itertools import count, islice
def A094400_gen(): # generator of terms
    def fib_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, 2):
        if fib_mod(m, m)==1 and fib_mod(m-1, m)!=0 and fib_mod(m+1, m)!=0:
            yield m
A094400_list = list(islice(A094400_gen(), 20)) # Chai Wah Wu, Jul 01 2026

Crossrefs

Cf. A069106, A069107, A094394, A094401, A094402.

Sequence in context: A179574 A229419 A116239 * A116282 A187958 A052050

Adjacent sequences: A094397 A094398 A094399 * A094401 A094402 A094403

Keyword

nonn

Author

Eric Rowland, May 01 2004

Extensions

Offset corrected by and a(15)-a(31) from Giovanni Resta, Jul 20 2013

Status

approved