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A060728
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Numbers n such that Ramanujan's equation x^2 + 7 = 2^n has an integer solution.
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7
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OFFSET
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1,1
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COMMENTS
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See A038198 for corresponding x. - Lekraj Beedassy, Sep 07 2004
Also numbers such that 2^(n-3)-1 is in A000217, i.e. a triangular number. - M. F. Hasler, Feb 23 2009
With respect to M. F. Hasler's comment above, all terms 2^(n-3) - 1 are known as the Ramanujan-Nagell triangular numbers (A076046). - Raphie Frank, Mar 31 2013
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REFERENCES
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J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 181, p. 56, Ellipses, Paris 2008.
J. Roberts, Lure of the Integers. pp. 90-91, MAA 1992.
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]
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LINKS
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Table of n, a(n) for n=1..5.
Anonymous, Developing a general 2nd degree Diophantine Equation x^2 + p = 2^n
M. Beeler, R. W. Gosper and R. Schroeppel, HAKMEM: item 31: A Ramanujan Problem (R. Schroeppel)
T. Do, Developing A General 2nd Degree Diophantine Equation x^2 + p = 2^n
G. Myerson, Bibliography
S. Ramanujan, Journal of the Indian Mathematical Society, Question 464(v,120)
Eric Weisstein's World of Mathematics, Ramanujan's Square Equation
Eric Weisstein's World of Mathematics, Diophantine Equation 2nd Powers
Wikipedia, Diophantine equation
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EXAMPLE
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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.
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MATHEMATICA
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ok[n_] := Reduce[x^2 + 7 == 2^n, x, Integers] =!= False; Select[ Range[100], ok] (* Jean-François Alcover, Sep 21 2011 *)
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CROSSREFS
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Cf. A038198.
Sequence in context: A192269 A101759 A089560 * A216433 A101761 A035359
Adjacent sequences: A060725 A060726 A060727 * A060729 A060730 A060731
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KEYWORD
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fini,full,nonn
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AUTHOR
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Lekraj Beedassy, Apr 25 2001
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EXTENSIONS
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Added keyword "full", M. F. Hasler, Feb 23 2009
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STATUS
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approved
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