A095081 Fibodd primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with one.

17, 19, 43, 53, 59, 61, 67, 101, 103, 127, 137, 163, 179, 197, 211, 229, 239, 263, 271, 281, 307, 313, 331, 347, 349, 373, 383, 389, 433, 449, 457, 467, 491, 499, 509, 569, 577, 593, 601, 619, 643, 653, 661, 677, 739, 773, 787, 797, 821, 823

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 A003622. Union of A095086 and A095089. Cf. A095061, A095080.

Programs

Mathematica

r = Map[Fibonacci, Range[2, 12]]; Select[Prime@ Range@ 144, Last@ Flatten@ Map[Position[r, #] &, Abs@ Differences@ NestWhileList[Function[k, k - SelectFirst[Reverse@ r, # < k &]], # + 1, # > 1 &]] == 1 &] (* Michael De Vlieger, Mar 27 2016, Version 10 *)

PARI

genit(maxx)={for(n=1,maxx,q=(n-1)+(n+sqrtint(5*n^2))\2; if(isprime(q), print1(q,",")));} \\ Bill McEachen, Mar 26 2016

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