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A095080 Fibeven primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with zero. 4


%S 2,3,5,7,11,13,23,29,31,37,41,47,71,73,79,83,89,97,107,109,113,131,

%T 139,149,151,157,167,173,181,191,193,199,223,227,233,241,251,257,269,

%U 277,283,293,311,317,337,353,359,367,379,397,401,409,419,421

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

%H Alois P. Heinz, <a href="/A095080/b095080.txt">Table of n, a(n) for n = 1..10000</a>

%H A. Karttunen and J. Moyer, <a href="/A095062/a095062.c.txt">C-program for computing the initial terms of this sequence</a>

%p F:= combinat[fibonacci]:

%p b:= proc(n) option remember; local j;

%p if n=0 then 0

%p else for j from 2 while F(j+1)<=n do od;

%p b(n-F(j))+2^(j-2)

%p fi

%p end:

%p a:= proc(n) option remember; local p;

%p p:= `if`(n=1, 1, a(n-1));

%p do p:= nextprime(p);

%p if b(p)::even then break fi

%p od; p

%p end:

%p seq(a(n), n=1..100); # _Alois P. Heinz_, Mar 27 2016

%o (Python)

%o from sympy import fibonacci, primerange

%o def a(n):

%o k=0

%o x=0

%o while n>0:

%o k=0

%o while fibonacci(k)<=n: k+=1

%o x+=10**(k - 3)

%o n-=fibonacci(k - 1)

%o return x

%o def ok(n):

%o return str(a(n))[-1]=="0"

%o print([n for n in primerange(1, 1001) if ok(n)]) # _Indranil Ghosh_, Jun 07 2017

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

%K nonn

%O 1,1

%A _Antti Karttunen_, Jun 01 2004

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Last modified June 19 15:58 EDT 2021. Contains 345144 sequences. (Running on oeis4.)