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A155072 Positive integers n such that the base-2 MR-expansion of 1/n is periodic with period (n-1)/4. 3
17, 41, 97, 137, 193, 313, 401, 409, 449, 521, 569, 761, 769, 809, 857, 929, 977 (list; graph; refs; listen; history; text; internal format)
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 A089637

Adjacent sequences:  A155069 A155070 A155071 * A155073 A155074 A155075

KEYWORD

nonn,more

AUTHOR

John W. Layman, Jan 19 2009

STATUS

approved

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Last modified January 20 02:29 EST 2018. Contains 297938 sequences.