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A060324
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a(n) is the minimal prime q such that n*(q+1)-1 is prime, that is, the smallest prime q so that n = (p+1)/(q+1) with p prime; or a(n) = -1 if no such q exists.
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11
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2, 2, 3, 2, 3, 2, 5, 2, 5, 2, 3, 3, 7, 2, 3, 2, 3, 2, 5, 2, 3, 5, 5, 2, 5, 3, 3, 2, 5, 2, 13, 3, 3, 2, 3, 2, 11, 2, 5, 5, 3, 3, 5, 2, 3, 2, 5, 3, 5, 2, 19, 5, 3, 7, 7, 2, 3, 2, 5, 2, 7, 11, 3, 2, 5, 2, 5, 3, 11, 5, 3, 5, 13, 5, 5, 2, 3, 2, 7, 2, 7, 5, 3, 2, 5, 2, 3, 2, 17, 2, 7, 3, 5, 2, 3, 3, 11, 2, 5, 5
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OFFSET
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1,1
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COMMENTS
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A conjecture of Schinzel, if true, would imply that such a q always exists.
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LINKS
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FORMULA
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EXAMPLE
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1 = (2+1)/(2+1), so the first term is 2; 3(2+1) - 1 = 8 which is not prime, yet 3(3+1) - 1 = 11 is prime (3 = (11+1)/(3+1)) so the 3rd term is 3.
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MAPLE
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a:= proc(n) local q;
q:= 2;
while not isprime(n*(q+1)-1) do
q:= nextprime(q);
od; q
end:
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MATHEMATICA
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a[n_] := (q = 2; While[!PrimeQ[n*(q + 1) - 1], q = NextPrime[q]]; q); a /@ Range[100] (* Jean-François Alcover, Jul 20 2011, after Maple prog. *)
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PROG
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(Haskell)
a060324 n = head [q | q <- a000040_list, a010051' (n * (q + 1) - 1) == 1]
(PARI) a(n) = {my(q=2); while (!isprime(n*(q+1)-1), q = nextprime(q+1)); q; } \\ Michel Marcus, Nov 20 2017
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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STATUS
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approved
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