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A361902
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Least k such that n+A000045(k) is prime, or -1 if no such k exists.
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7
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3, 1, 0, 0, 1, 0, 1, 0, 4, 3, 1, 0, 1, 0, 4, 3, 1, 0, 1, 0, 4, 3, 1, 0, 5, 9, 4, 3, 1, 0, 1, 0, 5, 6, 4, 3, 1, 0, 4, 3, 1, 0, 1, 0, 4, 3, 1, 0, 5, 9, 4, 3, 1, 0, 5, 9, 4, 3, 1, 0, 1, 0, 5, 6, 4, 3, 1, 0, 4, 3, 1, 0, 1, 0, 5, 6, 4, 3, 1, 0, 4, 3, 1, 0, 5, 12, 4
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OFFSET
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0,1
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COMMENTS
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When n >= 3 and a(n) != -1, a(n) is divisible by 3 if and only if n is odd, because A000045(k) is even if and only if k is divisible by 3.
The least n for which a(n) = -1 is one of 7123, 11009, and 14475. When n is 7123 or 11009, either a(n) > 60000 or a(n) = -1.
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LINKS
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FORMULA
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a(n) = 0 if and only if n is prime.
a(n) = -1 if n == 14475 (mod m), where m = 2*3*5*7*11*23*31 = 1647030 (see Gerbicz link).
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EXAMPLE
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The first Fibonacci number F such that 25+F is prime is F = 34 = A000045(9), so a(25) = 9.
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MATHEMATICA
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a[n_] := Module[{k = 0}, While[! PrimeQ[n + Fibonacci[k]], k++]; k]; Array[a, 100, 0] (* Amiram Eldar, Mar 30 2023 *)
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PROG
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(Python)
from sympy import isprime, fibonacci
from itertools import count
# Note: the function hangs if a(n) = -1.
return next(k for k in count() if isprime(n+fibonacci(k)))
(PARI) a(n) = my(k=0); while (!isprime(n+fibonacci(k)), k++); k; \\ Michel Marcus, Mar 30 2023
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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