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

%I A088733 #23 Feb 16 2025 08:32:51
%S A088733 3,11,19,79,41,167,127,233,179,461,227,883,433,569,719,1801,593,1861,
%T A088733 859,1553,1319,3863,1103,3499,2027,3671,2239,6089,1499,6323,3583,5147,
%U A088733 3739,5879,2843,11173,4597,7253,4799,14923,3779,14533,6599,7919,7589
%N A088733 n-th prime in the arithmetic progression n+k*(n+1) with k>0.
%H A088733 T. D. Noe, <a href="/A088733/b088733.txt">Table of n, a(n) for n = 1..10000</a>
%H A088733 T. D. Noe, <a href="/A088733/a088733.png">Linear Plot</a>
%H A088733 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletsTheorem.html">Dirichlet's Theorem</a>
%H A088733 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%e A088733 n=4, the progression starts: 4, 9, 14, 19, 24, 29, 34, 39, 44, 49,
%e A088733 54, 59, 64, 69, 74, 79, 84, 89, etc., with primes 19, 29, 59, 79, 89, etc.,
%e A088733 79 is the fourth prime: a(4)=79.
%t A088733 Table[k = 1; Do[While[p = n + k*(n + 1); ! PrimeQ[p], k++]; k++, {n}]; p, {n, 100}] (* _T. D. Noe_, Oct 20 2011 *)
%o A088733 (Haskell)
%o A088733 a088733 n = last $ take n $
%o A088733             [q | q <- [2 * n + 1, 3 * n + 2 ..], a010051' q == 1]
%o A088733 -- _Reinhard Zumkeller_, Oct 01 2014
%Y A088733 Cf. A088732.
%Y A088733 Cf. A010051.
%K A088733 nonn
%O A088733 1,1
%A A088733 _Reinhard Zumkeller_, Oct 12 2003