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A095080
Fibeven primes, i.e., primes p whose Zeckendorf-expansion A014417(p) ends with zero.
4
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
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 01 2004
STATUS
approved