A103961 Least k such that 2*n*k - 1 is a prime.

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

Offset: 1

Author

Lei Zhou, Feb 23 2005

Keywords

• easy
• nonn

Comments

Question: Is the sequence unbounded (like A016014)? - Dmitry Kamenetsky, Oct 26 2016

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

Examples

			2*1*2-1 = 3, so a(1) = 2;
2*5*2-1 = 19, so a(5) = 2.
		

Links

• Dmitry Kamenetsky, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A016014.

Programs

Mathematica

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 *)

PARI

a(n) = {my(k=1); while (!isprime(2*n*k-1), k++); k;} \\ Michel Marcus, Oct 27 2016