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A146351 Primes p such that continued fraction of (1 + sqrt(p))/2 has period 6: primes in A146331. 1
19, 59, 107, 131, 499, 659, 1627, 1907, 2251, 2467, 3803, 4139, 4283, 5827, 6779, 9539, 10067, 11491, 12619, 13763, 16987, 18587, 18803, 19507, 22003, 23003, 23819, 24859, 28643, 30859, 37507, 40939, 42083, 42299, 43403, 43867, 44563, 52747, 53507, 55339 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..40.

MAPLE

A146326 := proc(n) if not issqr(n) then numtheory[cfrac]( (1+sqrt(n))/2, 'periodic', 'quotients') ; nops(%[2]) ; else 0 ; fi; end: isA146351 := proc(n) RETURN(isprime(n) and A146326(n) = 6) ; end: for n from 2 to 13000 do if isA146351(n) then printf("%d, \n", n) ; fi; od: # R. J. Mathar, Sep 06 2009

MATHEMATICA

$MaxExtraPrecision = 4000; s = 10; aa = {}; Do[k = ContinuedFraction[(1 + Sqrt[Prime[n]])/2, 3000]; 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]] || k[[s + 4 m]] != k[[s + 5 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]] || k[[s + 4 m]] != k[[s + 5 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]] || k[[s + 4 m]] != k[[s + 5 m]]; AppendTo[aa, m]], {n, 1, 1495}]; bb = {}; Do[If[aa[[n]] == 6, AppendTo[bb, Prime[n]]], {n, 1, Length[aa]}]; bb (* Artur Jasinski *)

Select[Prime[Range[10000]], Length[ContinuedFraction[(1+Sqrt[#])/2][[2]]] == 6&] (* Harvey P. Dale, Dec 22 2013 *)

CROSSREFS

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

Sequence in context: A141773 A250024 A031375 * A139920 A182475 A142190

Adjacent sequences:  A146348 A146349 A146350 * A146352 A146353 A146354

KEYWORD

nonn

AUTHOR

Artur Jasinski, Oct 30 2008

EXTENSIONS

797 removed by R. J. Mathar, Sep 06 2009

More terms from Harvey P. Dale, Dec 22 2013

STATUS

approved

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