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Search: id:A146359
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| A146359 |
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Primes p such that continued fraction of (1+Sqrt[p])/2 has period 14 : primes in A146337. |
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2
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| 179, 251, 307, 347, 467, 587, 683, 1987, 5099, 5683, 7883, 8059, 8707, 12227, 14867, 15083, 15227
(list; graph; listen)
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OFFSET
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1,1
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MAPLE
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A := proc(n) local c; try c := numtheory[cfrac](1/2+sqrt(n)/2, 'periodic, quotients') ; RETURN(nops(c[2]) ); catch: RETURN(-1) end try ; end: isA146337 := proc(n) if A(n) = 14 then RETURN(true); else RETURN(false); fi; end: isA146359 := proc(n) RETURN(isprime(n) and isA146337(n)) ; end: for k from 1 do if isA146359(ithprime(k)) then printf("%d, ", ithprime(k)) ; fi; od: [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2008]
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MATHEMATICA
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$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]] == 14, AppendTo[bb, Prime[n]]], {n, 1, Length[aa]}]; bb (*Artur Jasinski*)
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CROSSREFS
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A000290, A050950-A050969, A078370, A146326-A146345, A146348-A146360.
Sequence in context: A108384 A162164 A142028 this_sequence A142441 A142492 A142670
Adjacent sequences: A146356 A146357 A146358 this_sequence A146360 A146361 A146362
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Oct 30 2008
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EXTENSIONS
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5813 and 6791 removed, extended beyond 8707 by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 08 2008
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