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%I #13 Feb 11 2023 11:31:34
%S 5,37,677,8837,98597,972197,9985601,99800101,999444997,9999200017,
%T 99986234437,999920001601,9999799764517,99999200001601,
%U 999999202999697,9999993200001157,99999979750774757,999999848000005777
%N a(n) is the largest prime of the form x^2 + 1 <= 10^n.
%C It is conjectured that the number of primes of the form x^2+1 is infinite and thus this sequence does not become a constant, but this has not been proved. It is easily shown that all terms greater than 5 end in 1 or 7.
%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 17.
%D P. Ribenboim, The Little Book of Big Primes. Springer-Verlag, 1991, p. 190.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LandausProblems.html">Landau's Problems.</a>
%t Do[ k = Floor[ Sqrt[ 10^n] - 1]; While[ !PrimeQ[k^2 + 1], k-- ]; Print[k^2 + 1], {n, 1, 19}]
%t lpf[n_]:=Module[{p=NextPrime[10^n,-1]},While[!IntegerQ[Sqrt[p-1]],p= NextPrime[ p,-1]];p]; Array[lpf,10] (* The program generates the first 10 terms of the sequence. *) (* _Harvey P. Dale_, Feb 11 2023 *)
%Y Cf. A005574, A002496, A083844, A083845, A083847, A083848, A083849.
%K nonn
%O 1,1
%A _Harry J. Smith_, May 05 2003
%E Edited and extended by _Robert G. Wilson v_, May 08 2003
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