A095083 - OEIS

%I #24 Feb 07 2023 05:55:00

%S 2,3,5,13,17,19,31,41,43,59,61,71,73,79,89,103,107,113,131,151,167,

%T 173,179,181,191,197,211,227,229,233,239,251,257,269,293,307,313,347,

%U 349,353,367,383,401,419,431,433,449,457,463,467,479,487,491

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

%H Amiram Eldar, <a href="/A095083/b095083.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..656 from Indranil Ghosh)

%H Antti Karttunen and John Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>.

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

%o (Python)

%o from sympy import fibonacci, primerange

%o def a(n):

%o     k=0

%o     x=0

%o     while n>0:

%o         k=0

%o         while fibonacci(k)<=n: k+=1

%o         x+=10**(k - 3)

%o         n-=fibonacci(k - 1)

%o     return x

%o def ok(n): return str(a(n)).count("1")%2

%o print([n for n in primerange(1, 1001) if ok(n)]) # _Indranil Ghosh_, Jun 08 2017

%Y Intersection of A000040 and A020899.

%Y Cf. A014417, A095084, A095063.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 01 2004