Search: id:A060728
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%I A060728
%S A060728 3,4,5,7,15
%N A060728 Numbers n such that Ramanujan's equation x^2 + 7 = 2^n has an integer 
               solution.
%C A060728 See A038198 for corresponding x. - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Sep 07 2004
%C A060728 Also numbers such that 2^(n-3)-1 is in A000217, i.e. a triangular number. 
               - M. F. Hasler, Feb 23 2009
%D A060728 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 181, p. 56, Ellipses, 
               Paris 2008.
%D A060728 J. Roberts, Lure of the Integers. pp. 90-91, MAA 1992.
%D A060728 T. Skolem, S. Chowla and D. J. Lewis, "The Diophantine Equation 2^(n+2)-7=x^2 
               and Related Problems.", Proc. Amer. Math. Soc. 10 (1959) 663-669, 
               available at http://www.jstor.org/stable/2033452 [M. F. Hasler, Feb 
               23 2009]
%H A060728 Anonymous, <a href="http://www.biochem.okstate.edu/OAS/OJAS/thiendo.htm">
               Developing a general 2nd degree Diophantine Equation x^2 + p = 2^n</
               a>
%H A060728 M. Beeler, R. W. Gosper and R. Schroeppel, <a href="http://www.inwap.com/
               pdp10/hbaker/hakmem/number.html#item31">HAKMEM: item 31: A Ramanujan 
               Problem (R. Schroeppel)</a>
%H A060728 T. Do, <a href="http://ojas.ucok.edu/98/T98/THIENDO.HTM">Developing A 
               General 2nd Degree Diophantine Equation x^2 + p = 2^n</a>
%H A060728 G. Myerson, <a href="http://www.mathematik.uni-bielefeld.de/~sillke/PUZZLES/
               ramanujan-nagell">Bibliography</a>
%H A060728 S. Ramanujan, Journal of the Indian Mathematical Society, <a href="http:/
               /www.imsc.res.in/~rao/ramanujan/collectedpapers/question/q464.htm">
               Question 464(v,120)</a>
%H A060728 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RamanujansSquareEquation.html">Link to a section of The World of 
               Mathematics</a>
%H A060728 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               DiophantineEquation2ndPowers.html">Diophantine Equation 2nd Powers</
               a>
%e A060728 The fifth and ultimate solution to Ramanujan's equation is obtained for 
               the 15-th power of 2, so that we have x^2 + 7 = 2^15 yielding x = 
               181.
%Y A060728 Cf. A038198.
%Y A060728 Sequence in context: A079463 A101759 A089560 this_sequence A101761 A035359 
               A143593
%Y A060728 Adjacent sequences: A060725 A060726 A060727 this_sequence A060729 A060730 
               A060731
%K A060728 fini,full,nonn
%O A060728 1,1
%A A060728 Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 25 2001
%E A060728 Added keyword "full" and reference to Skolem et al. - M. F. Hasler (MHasler(AT)univ-ag.fr), 
               Feb 23 2009

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