A088732 First prime in the arithmetic progression n+k*(n+1) with k>0.

2, 3, 5, 7, 19, 11, 13, 23, 17, 19, 43, 23, 103, 41, 29, 31, 67, 53, 37, 59, 41, 43, 137, 47, 149, 103, 53, 83, 173, 59, 61, 127, 131, 67, 139, 71, 73, 113, 233, 79, 163, 83, 257, 131, 89, 137, 281, 191, 97, 149, 101, 103, 211, 107, 109, 167, 113, 173, 353, 179

Offset: 0

Author

Reinhard Zumkeller, Oct 12 2003

Keywords

• nonn

Examples

			For n=10, the progression starts: 10, 21, 32, 43, 54, 65, 76, 87, 98, 109, etc., 43 is the first prime: a(10)=43.
		

Links

• T. D. Noe, Table of n, a(n) for n = 0..10000
• Eric Weisstein's World of Mathematics, Dirichlet's Theorem
• Eric Weisstein's World of Mathematics, Linnik's Theorem
• Wikipedia, Linnik's theorem
• Index entries for sequences related to primes in arithmetic progressions

Crossrefs

Cf. A088733.

Cf. A010051.

Programs

Haskell

a088732 n = head [q | q <- [2 * n + 1, 3 * n + 2 ..], a010051' q == 1]
-- Reinhard Zumkeller, Oct 01 2014

Mathematica

Table[k = 1; While[p = n + k*(n + 1); ! PrimeQ[p], k++]; p, {n, 0, 100}] (* Frank M Jackson, Oct 20 2011 *)

Python

from itertools import accumulate, repeat
from sympy import isprime
def A088732(n): return next(m for m in accumulate(repeat(n+1),initial=(n<<1)+1) if isprime(m)) # Chai Wah Wu, Aug 02 2023