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%I #30 Jan 15 2024 08:55:03
%S 1,2,3,7,29,59,709,2837,22697,590123,1180247,9441977,169955587,
%T 2719289393,5438578787,32631472723,391577672677,1566310690709,
%U 50121942102689,1503658263080671,9021949578484027,360877983139361081,21652678988361664861,476358937743956626943,5716307252927479523317
%N a(0) = 1; for n>0, a(n) = smallest prime of the form k*a(n-1) + 1.
%C Dirichlet proved that for every prime p there exists at least one prime of the form k*p + 1, hence the sequence is infinite.
%H T. D. Noe, <a href="/A061092/b061092.txt">Table of n, a(n) for n = 0..100</a>
%H Lejeune-Dirichlet, <a href="http://arxiv.org/abs/0808.1408">There are infinitely many prime numbers in all arithmetic progressions with first term and difference coprime</a>, arXiv:0808.1408 [math.HO], 2008-2014 (original 1837, translated from German).
%H Amarnath Murthy, <a href="http://fs.gallup.unm.edu/SNJ11.pdf">On the divisors of Smarandache Unary Sequence</a>. Smarandache Notions Journal, Vol. 11, No. 1-2-3, Spring 2000, page 184.
%e 59 = 2*29 + 1; 709 = 12*59 + 1.
%t a[1] = 2; a[n_] := a[n] = Block[{k = 1, p = a[n - 1]}, While[ !PrimeQ[k*p + 1], k++ ]; k*p + 1]; Table[ a[n], {n, 21}] (* _Robert G. Wilson v_, Nov 26 2004 *)
%o (PARI) for (n=0, 100, if (n>0, k=1; while (!isprime(k*a + 1), k++); a=k*a + 1, a=1); write("b061092.txt", n, " ", a)) \\ _Harry J. Smith_, Jul 17 2009
%Y Corresponding values of k are in A121799.
%K nonn
%O 0,2
%A _Amarnath Murthy_, Apr 19 2001
%E More terms from _Patrick De Geest_, May 29 2001
%E Edited by _Charles R Greathouse IV_, Aug 02 2010
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