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

1,1

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

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A334041 A181172 A075430 * A350179 A229289 A087634

Adjacent sequences: A095077 A095078 A095079 * A095081 A095082 A095083

Keyword

nonn

Author

Antti Karttunen, Jun 01 2004

Status

approved