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A103961
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Least k such that 2*n*k - 1 is a prime.
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2
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2, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 4, 3, 1, 1, 2, 2, 1, 2, 1, 1, 3, 1, 3, 2, 1, 3, 3, 1, 1, 2, 2, 1, 2, 1, 1, 2, 3, 1, 2, 1, 3, 3, 1, 4, 3, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 3, 3, 2, 4, 5, 2, 1, 3, 1, 3, 2, 1, 1, 2, 3, 7, 3, 1, 1, 2, 2, 1, 3, 4, 1, 2, 1, 3, 5, 1, 7, 8, 1, 1, 2, 3, 3, 2, 1, 1, 3, 1, 1, 5, 5, 3, 5, 2
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OFFSET
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1,1
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COMMENTS
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Answer: Yes. Essentially the same argument works. To get n such that a(n) > K, take distinct odd primes p_k, k=1..K with p_k not dividing k, and take n such that n == (2*k)^(-1) mod p_k and 2*k*n-1 > p_k for k=1..K. - Robert Israel, Oct 27 2016
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LINKS
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EXAMPLE
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2*1*2-1 = 3, so a(1) = 2;
2*5*2-1 = 19, so a(5) = 2.
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MATHEMATICA
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Do[k = 1; cp = n*k - 1; While[ ! PrimeQ[cp], k++; cp = n*k - 1]; Print[k], {n, 2, 400, 2}]
lkp[n_]:=Module[{k=1}, While[!PrimeQ[2n*k-1], k++]; k]; Array[lkp, 120] (* Harvey P. Dale, Nov 13 2020 *)
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PROG
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(PARI) a(n) = {my(k=1); while (!isprime(2*n*k-1), k++); k; } \\ Michel Marcus, Oct 27 2016
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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