Search: id:A005574
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%I A005574 M1010
%S A005574 1,2,4,6,10,14,16,20,24,26,36,40,54,56,66,74,84,90,94,110,116,120,
%T A005574 124,126,130,134,146,150,156,160,170,176,180,184,204,206,210,224,
%U A005574 230,236,240,250,256,260,264,270,280,284,300,306,314,326,340,350
%N A005574 Numbers n such that n^2 + 1 is prime.
%C A005574 Hardy and Littlewood conjectured that the asymptotic number of elements 
               in this sequence not exceeding n is approximately c*sqrt(n)/ln(n) 
               for some constant c. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 06 2006
%D A005574 R. K. Guy, "Unsolved Problems in Number Theory", 3rd edition, A2
%D A005574 G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 
               5th ed., Oxford Univ. Press, 1979, th. 17.
%D A005574 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005574 T. D. Noe, <a href="b005574.txt">Table of n, a(n) for n=1..10000</a>
%H A005574 F. Ellermann, <a href="a002496.txt">Primes of the form (m^2)+1 up to 
               10^6</a>
%H A005574 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               LandausProblems.html">Link to a section of The World of Mathematics.</
               a>
%H A005574 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Power.html">Link to a section of The World of Mathematics.</a>
%H A005574 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Near-SquarePrime.html">Near-Square Prime</a>
%H A005574 Marek Wolf, <a href="http://arXiv.org/abs/0803.1456">Search for primes 
               of the form m^2+1</a>
%t A005574 Select[Range[350], PrimeQ[ #^2 + 1] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Apr 06 2006
%Y A005574 a(n) = A090693(n)-1.
%Y A005574 Cf. A002522, A001912, A002496, A062325, A090693.
%Y A005574 Cf. A000068, A006314, A006313, A006315, A006316, A056994, A056995
%Y A005574 Sequence in context: A104692 A066755 A089238 this_sequence A109807 A125964 
               A139544
%Y A005574 Adjacent sequences: A005571 A005572 A005573 this_sequence A005575 A005576 
               A005577
%K A005574 nonn,easy,nice
%O A005574 1,2
%A A005574 N. J. A. Sloane (njas(AT)research.att.com).

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