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A230359
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Prime numbers p such that their Fibonacci entry points are less than p+1.
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4
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5, 11, 13, 17, 19, 29, 31, 37, 41, 47, 53, 59, 61, 71, 73, 79, 89, 97, 101, 107, 109, 113, 131, 137, 139, 149, 151, 157, 173, 179, 181, 191, 193, 197, 199, 211, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 373, 379, 389, 397, 401, 409, 419, 421, 431, 433, 439, 449, 457, 461, 479, 491, 499
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OFFSET
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1,1
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COMMENTS
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For these primes p there exists a Fibonacci like sequence that doesn't contain multiples of p.
For other primes p the Fibonacci entry points are p+1. These primes are sequence A000057: Primes dividing all Fibonacci sequences.
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LINKS
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FORMULA
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MAPLE
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filter:= proc(n) local i, a, b, c;
if not isprime(n) then return false fi;
a:= 0; b:= 1;
for i from 1 to n-1 do
c:= b;
b:= a+b mod n; if b = 0 then return true fi;
a:= c;
od;
false
end proc:
select(filter, [seq(i, i=3..1000, 2)]); # Robert Israel, Sep 01 2020
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MATHEMATICA
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A001177[n_] := For[k = 1, True, k++, If[Divisible[Fibonacci[k], n], Return[k]]]; A230359 = Reap[For[p = 2, p <= 499, p = NextPrime[p], If[A001177[p] < 1+p, Sow[p]]]][[2, 1]] (* Jean-François Alcover, Oct 21 2013 *)
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PROG
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(Sage)
def isA230359(p):
return any(p.divides(fibonacci(k)) for k in (1..p))
print([p for p in primes(1, 500) if isA230359(p)]) # Peter Luschny, Nov 01 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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