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A146326 Length of the period of the continued fraction of (1+sqrt(n))/2. 39
0, 2, 2, 0, 1, 4, 4, 4, 0, 2, 2, 2, 1, 4, 2, 0, 3, 6, 6, 4, 2, 6, 4, 4, 0, 2, 2, 4, 1, 2, 8, 4, 4, 4, 2, 0, 3, 6, 6, 8, 5, 4, 10, 6, 2, 8, 4, 4, 0, 2, 2, 4, 1, 6, 4, 2, 6, 6, 6, 4, 3, 4, 2, 0, 3, 6, 10, 6, 4, 6, 8, 4, 9, 6, 4, 8, 2, 4, 4, 4, 0, 2, 2, 2, 1, 6, 2, 8, 7, 2, 8, 8, 2, 12, 4, 8, 9, 4, 2, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First occurrence of n in this sequence see A146343.

Records see A146344.

Indices where records occurred see A146345.

a(n) =0 for n = k^2 (a(A000290(m+1)) = 0).

a(n) =1 for n = 4 k^2 + 4 k + 5 (a(A078370(m)) = 1).

a(n) =2 for n in A146327.

a(n) =3 for n in A146328.

a(n) =4 for n in A146329.

a(n) =5 for n in A146330.

a(n) =6 for n in A146331.

a(n) =7 for n in A146332.

a(n) =8 for n in A146333.

a(n) =9 for n in A146334.

a(n)=10 for n in A146335.

a(n)=11 for n in A146336.

a(n)=12 for n in A146337.

a(n)=13 for n in A146338.

a(n)=14 for n in A146339.

a(n)=15 for n in A146340.

a(n)=16 for n in A146341.

a(n)=17 for n in A146342.

LINKS

R. J. Mathar, Table of n, a(n) for n = 1..20000.

FORMULA

a(n) = 0 iff n is a square (A000290). - Robert G. Wilson v, Apr 11 2017

EXAMPLE

a(2) = 2 because continued fraction of (1+sqrt(2))/2 = 1, 4, 1, 4, 1, 4, 1, ... has period (1,4) length 2.

MAPLE

A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic', 'quotients') ; nops(%[2]) ; else 0 ; fi; end: seq(A146326(n), n=1..100) ; # R. J. Mathar, Sep 06 2009

MATHEMATICA

Table[cf = ContinuedFraction[(1 + Sqrt[n])/2]; If[Head[cf[[-1]]] === List, Length[cf[[-1]]], 0], {n, 100}]

f[n_] := Length@ ContinuedFraction[(1 + Sqrt[n])/2][[-1]]; Array[f, 100] (* Robert G. Wilson v, Apr 11 2017 *)

CROSSREFS

Cf. A000290, A078370, A146326-A146345.

Sequence in context: A214776 A317575 A295653 * A276727 A267617 A158852

Adjacent sequences:  A146323 A146324 A146325 * A146327 A146328 A146329

KEYWORD

nonn

AUTHOR

Artur Jasinski, Oct 30 2008

EXTENSIONS

a(39) and a(68) corrected by R. J. Mathar, Sep 06 2009

STATUS

approved

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Last modified July 19 03:54 EDT 2019. Contains 325144 sequences. (Running on oeis4.)