Search: id:A002383
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%I A002383 M2641 N1051
%S A002383 3,7,13,31,43,73,157,211,241,307,421,463,601,757,1123,1483,1723,2551,
%T A002383 2971,3307,3541,3907,4423,4831,5113,5701,6007,6163,6481,8011,8191,9901,
%U A002383 10303,11131,12211,12433,13807,14281,17293,19183,20023,20593,21757
%N A002383 Primes of form n^2 + n + 1.
%C A002383 Also primes p such that 4p-3 is square. - Giovanni Teofilatto (g.teofilatto(AT)tiscalinet.it), 
               Sep 07 2005
%C A002383 Also these primes are sums of 1 and some consecutive even numbers starting 
               at 2; e.g. 31=1+2+4+6+8+10. - Labos E. (labos(AT)ana.sote.hu), Apr 
               15 2003
%C A002383 Also primes of form n^2 - n + 1 (Prime central polygonal numbers, A002061). 
               - Zak Seidov (zakseidov(AT)yahoo.com), Jan 26 2006
%C A002383 also: Primes of the form : sum of Triangular numbers as: TriangularNumber(n)+TriangularNumber(n+2). 
               7=1+6, 13=3+10, 31=10+21, 43=15+28, 73=28+45, ... [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Apr 03 2009]
%C A002383 It is not known whether there are infinitely many primes of the form 
               n^2+n+1. H.E.Rose, A Course in Number Theory, Clarendon Press,1988, 
               p. 217. [From Daniel Tisdale (daniel6874(AT)gmail.com), Jun 27 2009]
%D A002383 D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 
               105, National Research Council, Washington, DC, 1941, p. 46.
%D A002383 L. Poletti, Le serie dei numeri primi appartenente alle due forme quadratiche 
               (A) n^2+n+1 e (B) n^2+n-1 ..., Atti della Reale Accademia Nazionale 
               dei Lincei, Memorie della Classe di Scienze Fisiche, Matematiche 
               e Naturali, s. 6. 3 (1929), 193-218.
%D A002383 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002383 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A002383 Zak Seidov, <a href="b002383.txt">Table of n, a(n) for n=1..10751</a>
%F A002383 a(n) = A002384(n)^2 + A002384(n) + 1 = (A088503(n-1)^2 + 3)/4 = (A110284(n) 
               + 3)/4. - Chandler
%t A002383 s=1; Do[s=s+2*n; If[PrimeQ[s], Print[{s, 2*n}]], {n, 1, 100}]
%t A002383 tr[a_]:=Module[{x},s=0;For[i=1,i<a,s+=i;i++ ];x=s];lst={};Do[a=tr[n];
               b=tr[n+2];p=a+b;If[PrimeQ[p],AppendTo[lst,p]],{n,4!}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Apr 03 2009]
%Y A002383 Cf. A002384, A088503, A110284.
%Y A002383 Sequence in context: A083520 A162869 A079018 this_sequence A163418 A161218 
               A068679
%Y A002383 Adjacent sequences: A002380 A002381 A002382 this_sequence A002384 A002385 
               A002386
%K A002383 nonn,easy
%O A002383 1,1
%A A002383 N. J. A. Sloane (njas(AT)research.att.com).
%E A002383 Extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 07 2005

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