A210620 Nontrivial solution to x = 2*x^2 - 1 mod 10^n.

7, 37, 937, 5937, 35937, 335937, 9335937, 19335937, 319335937, 7319335937, 77319335937, 877319335937, 9877319335937, 89877319335937, 389877319335937, 4389877319335937, 84389877319335937, 384389877319335937, 8384389877319335937, 88384389877319335937

Offset

1,1

Comments

The trivial solution is x = 1.

References

J. A. H. Hunter, Fun with Figures, Oxford University Press, 1956.

Links

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

Mathematica

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 *)

Prog

(PARI) a(n)=lift(chinese(Mod(1, 2^n), Mod(5^n\2, 5^n))) \\ Charles R Greathouse IV, Mar 28 2012

Crossrefs

Cf. A007185.

Sequence in context: A117731 A155010 A292807 * A250843 A078303 A127729

Adjacent sequences: A210617 A210618 A210619 * A210621 A210622 A210623

Keyword

base,easy,nonn

Author

Michael Brundage, Mar 27 2012

Status

approved