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

%I A095081 #25 May 06 2021 11:04:12
%S A095081 17,19,43,53,59,61,67,101,103,127,137,163,179,197,211,229,239,263,271,
%T A095081 281,307,313,331,347,349,373,383,389,433,449,457,467,491,499,509,569,
%U A095081 577,593,601,619,643,653,661,677,739,773,787,797,821,823
%N A095081 Fibodd primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with one.
%H A095081 Alois P. Heinz, <a href="/A095081/b095081.txt">Table of n, a(n) for n = 1..10000</a>
%H A095081 A. Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>
%t A095081 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 *)
%o A095081 (PARI)
%o A095081 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
%o A095081 (Python)
%o A095081 from sympy import fibonacci, primerange
%o A095081 def a(n):
%o A095081     k=0
%o A095081     x=0
%o A095081     while n>0:
%o A095081         k=0
%o A095081         while fibonacci(k)<=n: k+=1
%o A095081         x+=10**(k - 3)
%o A095081         n-=fibonacci(k - 1)
%o A095081     return x
%o A095081 def ok(n):
%o A095081     return str(a(n))[-1]=="1"
%o A095081 print([n for n in primerange(1, 1001) if ok(n)]) # _Indranil Ghosh_, Jun 07 2017
%Y A095081 Intersection of A000040 and A003622. Union of A095086 and A095089. Cf. A095061, A095080.
%K A095081 nonn
%O A095081 1,1
%A A095081 _Antti Karttunen_, Jun 01 2004