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%I #12 Apr 18 2014 11:12:30
%S 17,103,619,2477,34679,416149,7490683,29962733,419478263,5872695683,
%T 82217739563,986612874757,27625160493197,994505777755093,
%U 5967034666530559,71604415998366709,6444397439853003811,180443128315884106709,9743928929057741762287
%N a(1) = 17, a(n) is smallest prime of the form k*a(n - 1) + 1.
%C Sequence does not begin with 2 (17 = 8*2 + 1; all primes are k*2+1) because 3 = 1*2 + 1 or 5 = 2*2 + 1 are smaller; and they would lead to A061092, or A059411. Also: 7 belongs to A061092; 11 to A059411 and 13 is a(1) in A214523.
%H Harvey P. Dale, <a href="/A214632/b214632.txt">Table of n, a(n) for n = 1..300</a>
%e a(2) = 103 = 6*17 + 1.
%t t = {17}; Do[k = 1; While[p = k*t[[-1]] + 1; ! PrimeQ[p], k++]; AppendTo[t, p], {20}]; t (* _T. D. Noe_, Jul 24 2012 *)
%t nxt[n_]:=Module[{k=1},While[!PrimeQ[k*n+1],k++];k*n+1]; NestList[nxt,17,20] (* _Harvey P. Dale_, Apr 18 2014 *)
%Y Cf. A061092, A059411, A214523.
%K nonn
%O 1,1
%A _Robin Garcia_, Jul 23 2012
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