A155072 Positive integers n such that the base-2 MR-expansion of 1/n is periodic with period (n-1)/4.

17, 41, 97, 137, 193, 313, 401, 409, 449, 521, 569, 761, 769, 809, 857, 929, 977

Offset

1,1

Comments

See A136042 for the definition of the MR-expansion of a positive real number.

It appears that all terms of this sequence are primes of the form 8n+1 (A007519).

Links

Table of n, a(n) for n=1..17.

Example

Applying the definition of the base-2 MR-expansion to 1/17 gives 1/17->2/17->4/17->8/17->16/17->32/17->15/17->30/17->13/17->26/17->9/17->18/17->1/17->..., which shows that the expansion begins {5,1,1,1,...} and has period 4=(17-1)/4.

Mathematica

a[p_] := 1 + Sum[2 Cos[2^n Pi/((2 p + 1) )], {n, 1, p}];
Select[Range[500], Reduce[a[#]^2 == 2 # + 1, Integers] &];
2 % + 1 (* Gerry Martens, May 01 2016 *)

Crossrefs

Cf. A007519, A136042, A136043.

Sequence in context: A281792 A293394 A070179 * A243451 A145991 A139961

Adjacent sequences: A155069 A155070 A155071 * A155073 A155074 A155075

Keyword

nonn,more

Author

John W. Layman, Jan 19 2009

Status

approved