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A210620
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Nontrivial solution to x = 2*x^2 - 1 mod 10^n.
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1
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7, 37, 937, 5937, 35937, 335937, 9335937, 19335937, 319335937, 7319335937, 77319335937, 877319335937, 9877319335937, 89877319335937, 389877319335937, 4389877319335937, 84389877319335937, 384389877319335937, 8384389877319335937, 88384389877319335937
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OFFSET
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1,1
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COMMENTS
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The trivial solution is x = 1.
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REFERENCES
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J. A. H. Hunter, Fun with Figures, Oxford University Press, 1956.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..100
Gérard P. Michon, A decadic puzzle by J.A.H. Hunter (1902-1986)
Greg Ross, Futility Closet Math Note 93
Brent Yorgey, Math Less Traveled: A curiosity
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MATHEMATICA
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f[n_] := Module[{d}, digs = {7}; Do[d = Select[Range[0, 9], Module[{t}, t = digs~Prepend~#; FromDigits[t] == Mod[2 FromDigits[t]^2 - 1, 10^(Length[digs] + 1)]] &][[1]]; digs = digs~Prepend~d, {n}]; FromDigits[digs]]; Table[f[n - 1], {n, 10}] (* Brenton Bostick, Mar 27 2012 *)
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PROG
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(PARI) a(n)=lift(chinese(Mod(1, 2^n), Mod(5^n\2, 5^n))) \\ Charles R Greathouse IV, Mar 28, 2012
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CROSSREFS
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Cf. A007185.
Sequence in context: A082687 A117731 A155010 * A078303 A127729 A129736
Adjacent sequences: A210617 A210618 A210619 * A210621 A210622 A210623
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KEYWORD
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base,easy,nonn,changed
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AUTHOR
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Michael Brundage, Mar 27 2012
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STATUS
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approved
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