A095083 Fibodious primes, i.e., primes p whose Zeckendorf-expansion A014417(p) contains an odd number of 1-fibits.

2, 3, 5, 13, 17, 19, 31, 41, 43, 59, 61, 71, 73, 79, 89, 103, 107, 113, 131, 151, 167, 173, 179, 181, 191, 197, 211, 227, 229, 233, 239, 251, 257, 269, 293, 307, 313, 347, 349, 353, 367, 383, 401, 419, 431, 433, 449, 457, 463, 467, 479, 487, 491

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..656 from Indranil Ghosh)
• Antti Karttunen and John Moyer, C-program for computing the initial terms of this sequence.

Crossrefs

Intersection of A000040 and A020899.

Cf. A014417, A095084, A095063.

Programs

Mathematica

Select[Flatten[Position[Mod[DigitCount[Select[Range[0, 5000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 1]] - 1, PrimeQ] (* Amiram Eldar, Feb 07 2023 *)

Python

from sympy import fibonacci, primerange
def a(n):
    k=0
    x=0
    while n>0:
        k=0
        while fibonacci(k)<=n: k+=1
        x+=10**(k - 3)
        n-=fibonacci(k - 1)
    return x
def ok(n): return str(a(n)).count("1")%2
print([n for n in primerange(1, 1001) if ok(n)]) # Indranil Ghosh, Jun 08 2017