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

%I A095083 #24 Feb 07 2023 05:55:00
%S A095083 2,3,5,13,17,19,31,41,43,59,61,71,73,79,89,103,107,113,131,151,167,
%T A095083 173,179,181,191,197,211,227,229,233,239,251,257,269,293,307,313,347,
%U A095083 349,353,367,383,401,419,431,433,449,457,463,467,479,487,491
%N A095083 Fibodious primes, i.e., primes p whose Zeckendorf-expansion A014417(p) contains an odd number of 1-fibits.
%H A095083 Amiram Eldar, <a href="/A095083/b095083.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..656 from Indranil Ghosh)
%H A095083 Antti Karttunen and John Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>.
%t A095083 Select[Flatten[Position[Mod[DigitCount[Select[Range[0, 5000], BitAnd[#, 2 #] == 0 &], 2, 1], 2], 1]] - 1, PrimeQ] (* _Amiram Eldar_, Feb 07 2023 *)
%o A095083 (Python)
%o A095083 from sympy import fibonacci, primerange
%o A095083 def a(n):
%o A095083     k=0
%o A095083     x=0
%o A095083     while n>0:
%o A095083         k=0
%o A095083         while fibonacci(k)<=n: k+=1
%o A095083         x+=10**(k - 3)
%o A095083         n-=fibonacci(k - 1)
%o A095083     return x
%o A095083 def ok(n): return str(a(n)).count("1")%2
%o A095083 print([n for n in primerange(1, 1001) if ok(n)]) # _Indranil Ghosh_, Jun 08 2017
%Y A095083 Intersection of A000040 and A020899.
%Y A095083 Cf. A014417, A095084, A095063.
%K A095083 nonn
%O A095083 1,1
%A A095083 _Antti Karttunen_, Jun 01 2004