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Fib00 primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with two zeros.
2

%I #16 Nov 10 2021 17:07:43

%S 3,5,11,13,29,37,47,71,73,79,89,97,107,113,131,139,149,157,173,181,

%T 191,199,223,233,241,251,257,283,293,317,359,367,401,409,419,443,461,

%U 479,487,503,521,547,563,571,587,613,631,647,673,683,691,733

%N Fib00 primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with two zeros.

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

%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))[-2:]=="00"

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

%o (PARI) list(lim)=my(v=List(), w=quadgen(20), phi=(1+w)/2, p2=phi^2, x=(2*phi-2)*p2, q); lim=lim\1+1; while(x<lim, if(isprime(q=x\1), listput(v,q)); x+=p2); Vec(v) \\ _Charles R Greathouse IV_, Nov 10 2021

%Y Cf. A095062. Intersection of A000040 and A026274. Union of A095085 and A095088.

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 01 2004