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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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4
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OFFSET
| 1,1
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COMMENTS
| See A038198 for corresponding x. - Lekraj Beedassy (blekraj(AT)yahoo.com), 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
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REFERENCES
| 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
| 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, Link to a section of The World of Mathematics
Eric Weisstein's World of Mathematics, Diophantine Equation 2nd Powers
Wikipedia, Diophantine equation
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EXAMPLE
| 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
| ok[n_] := Reduce[x^2 + 7 == 2^n, x, Integers] =!= False; Select[ Range[100], ok] (* From Jean-François Alcover, Sep 21 2011 *)
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CROSSREFS
| Cf. A038198.
Sequence in context: A192269 A101759 A089560 * A101761 A035359 A143593
Adjacent sequences: A060725 A060726 A060727 * A060729 A060730 A060731
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KEYWORD
| fini,full,nonn,changed
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AUTHOR
| Lekraj Beedassy (blekraj(AT)yahoo.com), Apr 25 2001
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EXTENSIONS
| Added keyword "full" and reference to Skolem et al. - M. F. Hasler, Feb 23 2009
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