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

%I A095080 #23 Jul 01 2021 06:12:02
%S A095080 2,3,5,7,11,13,23,29,31,37,41,47,71,73,79,83,89,97,107,109,113,131,
%T A095080 139,149,151,157,167,173,181,191,193,199,223,227,233,241,251,257,269,
%U A095080 277,283,293,311,317,337,353,359,367,379,397,401,409,419,421
%N A095080 Fibeven primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with zero.
%H A095080 Alois P. Heinz, <a href="/A095080/b095080.txt">Table of n, a(n) for n = 1..10000</a>
%H A095080 A. Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>
%p A095080 F:= combinat[fibonacci]:
%p A095080 b:= proc(n) option remember; local j;
%p A095080       if n=0 then 0
%p A095080     else for j from 2 while F(j+1)<=n do od;
%p A095080          b(n-F(j))+2^(j-2)
%p A095080       fi
%p A095080     end:
%p A095080 a:= proc(n) option remember; local p;
%p A095080       p:= `if`(n=1, 1, a(n-1));
%p A095080       do p:= nextprime(p);
%p A095080          if b(p)::even then break fi
%p A095080       od; p
%p A095080     end:
%p A095080 seq(a(n), n=1..100);  # _Alois P. Heinz_, Mar 27 2016
%t A095080 F = Fibonacci;
%t A095080 b[n_] := b[n] = Module[{j},
%t A095080      If[n == 0, 0, For[j = 2, F[j + 1] <= n, j++];
%t A095080      b[n - F[j]] + 2^(j - 2)]];
%t A095080 a[n_] := a[n] = Module[{p},
%t A095080      p = If[n == 1, 1, a[n - 1]]; While[True,
%t A095080      p = NextPrime[p]; If[ EvenQ[b[p]], Break[]]]; p];
%t A095080 Array[a, 100] (* _Jean-François Alcover_, Jul 01 2021, after _Alois P. Heinz_ *)
%o A095080 (Python)
%o A095080 from sympy import fibonacci, primerange
%o A095080 def a(n):
%o A095080     k=0
%o A095080     x=0
%o A095080     while n>0:
%o A095080         k=0
%o A095080         while fibonacci(k)<=n: k+=1
%o A095080         x+=10**(k - 3)
%o A095080         n-=fibonacci(k - 1)
%o A095080     return x
%o A095080 def ok(n):
%o A095080     return str(a(n))[-1]=="0"
%o A095080 print([n for n in primerange(1, 1001) if ok(n)]) # _Indranil Ghosh_, Jun 07 2017
%Y A095080 Intersection of A000040 and A022342. Union of A095082 and A095087. Cf. A095060, A095081.
%K A095080 nonn
%O A095080 1,1
%A A095080 _Antti Karttunen_, Jun 01 2004