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A116934 First prime in the arithmetic progression (n+k*p: k>0), where p is the smallest coprime greater than n+1.

%I A116934 #11 Feb 16 2025 08:33:00
%S A116934 7,7,13,11,19,17,43,19,31,23,37,29,43,31,83,73,131,41,61,43,67,47,73,
%T A116934 53,79,113,317,59,277,67,97,67,103,71,109,241,193,79,367,83,127,89,
%U A116934 223,373,139,193,439,101,151,103,157,107,163,113,283,233,293,241,181,127,313
%N A116934 First prime in the arithmetic progression (n+k*p: k>0), where p is the smallest coprime greater than n+1.
%C A116934 a(n) = n + A116933(n)*A079578(n).
%H A116934 Reinhard Zumkeller, <a href="/A116934/b116934.txt">Table of n, a(n) for n = 1..10000</a>
%H A116934 <a href="/index/Pri#primes_AP">Index entries for sequences related to primes in arithmetic progressions</a>
%H A116934 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DirichletsTheorem.html">Dirichlet's Theorem.</a>
%o A116934 (Haskell)
%o A116934 a116934 n = head [q | k <- [1..], let q = n + k * a079578 n,
%o A116934                       a010051' q == 1]
%o A116934 -- _Reinhard Zumkeller_, Oct 01 2014
%Y A116934 Cf. A088732.
%Y A116934 Cf. A010051, A079578, A116933.
%K A116934 nonn
%O A116934 1,1
%A A116934 _Reinhard Zumkeller_, Feb 27 2006