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%I #47 Mar 11 2024 05:09:18
%S 1,3,5,11,181
%N Numbers n such that n^2 + 7 is a power of 2.
%C The exponents of the corresponding powers of 2 are 3, 4, 5, 7, 15 (see Ramanujan). - _N. J. A. Sloane_, Jun 01 2014
%C The terms lead to identities resembling Machin's Pi/4 = arctan(1/1) = 4*arctan(1/5) - arctan(1/239), for example, arctan(sqrt(7)/1) = 5*arctan(sqrt(7)/11) + 2*arctan(sqrt(7)/181), which can also be expressed as arcsin(sqrt(7/2^3)) = 5*arcsin(sqrt(7/2^7)) + 2*arcsin(sqrt(7/2^15)) (cf. A168229). - _Joerg Arndt_, Nov 09 2012
%D J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 181, p. 56, Ellipses, Paris 2008.
%D L. J. Mordell, Diophantine Equations, Academic Press, NY, 1969, p. 205.
%D S. Ramanujan, Collected Papers, Ed. G. H. Hardy et al., Cambridge 1927; Chelsea, NY, 1962. See Question 464, p. 327. - _N. J. A. Sloane_, Jun 01 2014
%H Spencer De Chenne, <a href="http://buzzard.ups.edu/courses/2013spring/projects/spencer-ant-ups-434-2013.pdf">The Ramanujan-Nagell Theorem: Understanding the Proof</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/RamanujansSquareEquation.html">Ramanujan's Square Equation</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Lucas_sequence">Lucas Sequence</a>
%t ok[n_] := Reduce[k>0 && n^2 + 7 == 2^k, k, Integers] =!= False; Select[Range[1000], ok] (* _Jean-François Alcover_, Sep 21 2011 *)
%o (PARI) [x | n<-[0..99], issquare(2^n-7,&x)] \\ _M. F. Hasler_, Mar 11 2024
%Y Cf. A060728, A002249, A107920.
%K nonn,fini,full
%O 1,2
%A _N. J. A. Sloane_
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