A088733 n-th prime in the arithmetic progression n+k*(n+1) with k>0.

3, 11, 19, 79, 41, 167, 127, 233, 179, 461, 227, 883, 433, 569, 719, 1801, 593, 1861, 859, 1553, 1319, 3863, 1103, 3499, 2027, 3671, 2239, 6089, 1499, 6323, 3583, 5147, 3739, 5879, 2843, 11173, 4597, 7253, 4799, 14923, 3779, 14533, 6599, 7919, 7589

Offset: 1

Author

Reinhard Zumkeller, Oct 12 2003

Keywords

• nonn

Examples

			n=4, the progression starts: 4, 9, 14, 19, 24, 29, 34, 39, 44, 49,
54, 59, 64, 69, 74, 79, 84, 89, etc., with primes 19, 29, 59, 79, 89, etc.,
79 is the fourth prime: a(4)=79.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• T. D. Noe, Linear Plot
• Eric Weisstein's World of Mathematics, Dirichlet's Theorem
• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Cf. A088732.

Cf. A010051.

Programs

Haskell

a088733 n = last $ take n $
            [q | q <- [2 * n + 1, 3 * n + 2 ..], a010051' q == 1]
-- Reinhard Zumkeller, Oct 01 2014

Mathematica

Table[k = 1; Do[While[p = n + k*(n + 1); ! PrimeQ[p], k++]; k++, {n}]; p, {n, 100}] (* T. D. Noe, Oct 20 2011 *)