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A322005
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Least prime p such that n + p is a Fibonacci number (A000045).
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2
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2, 2, 3, 2, 17, 3, 2, 137, 5, 601, 3, 2, 43, 131, 7, 19, 5, 17, 3, 2, 967, 13, 67, 11, 31, 927372692193078999151, 29, 7, 61, 5, 59, 3, 2, 577, 199, 109, 19, 107, 17, 571, 193, 103, 13, 101, 11, 2539, 43, 97, 7, 14930303, 5, 27777890035237, 3, 2, 179, 89, 6709, 10889, 31, 46309, 29, 83, 6703, 547, 313, 79, 23, 46301, 919, 541, 19, 73, 17
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OFFSET
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0,1
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COMMENTS
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See A322004 for the indices of the corresponding Fibonacci numbers, and further information.
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LINKS
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EXAMPLE
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a(0) = 2 is the smallest prime p such that p + 0 (= 2) is a Fibonacci number.
a(1) = 2 is the smallest prime p such that p + 1 (= 3) is a Fibonacci number.
a(2) = 3 is the smallest prime p such that p + 2 (= 5) is a Fibonacci number.
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MAPLE
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f:= proc(n) local p, k, a, b, c;
a:= -n:b:= 1-n:
do
c:= b;
b:= a+b+n;
a:= c;
if isprime(b) then return b fi
od
end proc:
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MATHEMATICA
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primeQ[n_] := n>0 && PrimeQ[n]; a[n_] := Module[{i=2}, While[!primeQ[Fibonacci[i] - n], i++]; Fibonacci[i] - n]; Array[a, 27, 0] (* Amiram Eldar, Dec 12 2018 *)
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PROG
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(PARI) a(n)=for(i=1, oo, ispseudoprime(fibonacci(i)-n)&&return(fibonacci(i)-n))
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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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