A095080 Fibeven primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with zero.

2, 3, 5, 7, 11, 13, 23, 29, 31, 37, 41, 47, 71, 73, 79, 83, 89, 97, 107, 109, 113, 131, 139, 149, 151, 157, 167, 173, 181, 191, 193, 199, 223, 227, 233, 241, 251, 257, 269, 277, 283, 293, 311, 317, 337, 353, 359, 367, 379, 397, 401, 409, 419, 421

Offset: 1

Author

Antti Karttunen, Jun 01 2004

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence

Crossrefs

Intersection of A000040 and A022342. Union of A095082 and A095087. Cf. A095060, A095081.

Programs

Maple

F:= combinat[fibonacci]:
b:= proc(n) option remember; local j;
      if n=0 then 0
    else for j from 2 while F(j+1)<=n do od;
         b(n-F(j))+2^(j-2)
      fi
    end:
a:= proc(n) option remember; local p;
      p:= `if`(n=1, 1, a(n-1));
      do p:= nextprime(p);
         if b(p)::even then break fi
      od; p
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Mar 27 2016

Mathematica

F = Fibonacci;
b[n_] := b[n] = Module[{j},
     If[n == 0, 0, For[j = 2, F[j + 1] <= n, j++];
     b[n - F[j]] + 2^(j - 2)]];
a[n_] := a[n] = Module[{p},
     p = If[n == 1, 1, a[n - 1]]; While[True,
     p = NextPrime[p]; If[ EvenQ[b[p]], Break[]]]; p];
Array[a, 100] (* Jean-François Alcover, Jul 01 2021, after Alois P. Heinz *)

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))[-1]=="0"
print([n for n in primerange(1, 1001) if ok(n)]) # Indranil Ghosh, Jun 07 2017