1,1

Something has gone wrong here - this is a subset of A146354. - N. J. A. Sloane (njas(AT)research.att.com), Oct 31 2008

For primes in this sequence see A146354.

Superset of A146354. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 2008]

a(1) = 73 because continued fraction of (1+Sqrt[73])/2 = 4, 1, 3, 2, 1, 1, 2, 3, 1, 7, 1, 3, 2, 1, 1, 2, 3, 1, 7, 1, 3, 2, 1, 1, 2, 3, 1, 7, 1, 3, ...

has period (1, 3, 2, 1, 1, 2, 3, 1, 7) length 9

isA143577 := proc(k) local c; try c := numtheory[cfrac](1/2+sqrt(k)/2, 'periodic', 'quotients') ; if nops(c[2]) = 9 then RETURN(true) ; else RETURN(false) ; fi; catch: RETURN(false) ; end try; end: for k from 2 to 80000 do if isA143577(k) then printf("%d, ", k) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 2008]

s = 10; aa = {}; Do[k = ContinuedFraction[(1 + Sqrt[n])/2, 1000]; If[Length[k] < 190, AppendTo[aa, 0], m = 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; s = s + 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; s = s + 1; While[k[[s ]] != k[[s + m]] || k[[s + m]] != k[[s + 2 m]] || k[[s + 2 m]] != k[[s + 3 m]] || k[[s + 3 m]] != k[[s + 4 m]], m++ ]; AppendTo[aa, m]], {n, 1, 500}]; bb = {}; Do[If[aa[[n]] == 9, AppendTo[bb, n]], {n, 1, Length[aa]}]; bb (*Artur Jasinski*)

A000290, A078370, A146326-A146345, A146348-A146360.

Sequence in context: A141375 A107008 A140621 this_sequence A146354 A050958 A139990

Adjacent sequences: A143574 A143575 A143576 this_sequence A143578 A143579 A143580

nonn

Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008

Extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 05 2008