%I A005846 M5273
%S A005846 41,43,47,53,61,71,83,97,113,131,151,173,197,223,251,281,313,347,383,
%T A005846 421,461,503,547,593,641,691,743,797,853,911,971,1033,1097,1163,1231,
%U A005846 1301,1373,1447,1523,1601,1847,1933,2111,2203,2297,2393,2591,2693,2797
%N A005846 Primes of form n^2 + n + 41.
%C A005846 Note that 41 is the largest of Euler's Lucky numbers (A014556). - Lekraj 
               Beedassy (blekraj(AT)yahoo.com), Apr 22 2004
%C A005846 a(n)=A117530(13,n) for n<=13: a(1)=A117530(13,1)=A014556(6)=41, A117531(13)=13. 
               - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 26 2006
%C A005846 The g.f. -(41-80*z+41*z**2)/(z-1)**3 conjectured by S. Plouffe in his 
               1992 dissertation is wrong.
%C A005846 The link to E. Wegrzynowski contents the following false statement: "It 
               is possible to find a polynomial of the form n^2 + n + B that gives 
               prime numbers for n = 0...A, A being any number." It is known that 
               the maximum is A = 39 for B = 41. - Luis Rodriguez (luiroto(AT)yahoo.com), 
               Jun 22 2008
%C A005846 Contrary to the last comment, Mollin's Theorem 2.1 shows that any A is 
               possible if the Prime k-tuples Conjecture is assumed. [From T. D. 
               Noe (noe(AT)sspectra.com), Aug 31 2009]
%D A005846 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A005846 P. Ribenboim, The Book of Prime Number Records. Springer-Verlag, NY, 
               2nd ed., 1989, p. 137.
%D A005846 R. A. Mollin, Prime producing quadratics, Amer. Math. Monthly 104 (1997), 
               529-544. [From T. D. Noe (noe(AT)sspectra.com), Aug 31 2009]
%H A005846 Zak Seidov, <a href="b005846.txt">Table of n, a(n) for n = 1..10000.</
               a>
%H A005846 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A005846 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%H A005846 E. Wegrzynowski, <a href="http://www.lifl.fr/~wegrzyno/FormulPrem/FormulesPremiers23.html">
               Les formules simples qui donnent des nombres premiers en grande quantite</
               a>
%H A005846 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Prime-GeneratingPolynomial.html">Link to a section of The World of 
               Mathematics.</a>
%F A005846 a(n) =A056561(n)^2+A056561(n)+41
%e A005846 a(39)=1601=39^2+39+41 is in the sequence because it is prime. 1681=40^2+40+41 
               is not because 1681=41*41.
%t A005846 lst={};Do[p=n^2+n+41;If[PrimeQ[p],AppendTo[lst,p]],{n,6!}];lst [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 05 2009]
%Y A005846 Cf. A048988, A007634, A056561, A002378, A007635.
%Y A005846 Sequence in context: A118124 A054057 A155884 this_sequence A154498 A062669 
               A045710
%Y A005846 Adjacent sequences: A005843 A005844 A005845 this_sequence A005847 A005848 
               A005849
%K A005846 nonn,easy
%O A005846 1,1
%A A005846 N. J. A. Sloane (njas(AT)research.att.com).
%E A005846 More terms from Henry Bottomley (se16(AT)btinternet.com), Jun 26 2000