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A077426
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Nonsquare integers n such that the continued fraction (sqrt(n)+1)/2 has odd period length.
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8
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5, 13, 17, 29, 37, 41, 53, 61, 65, 73, 85, 89, 97, 101, 109, 113, 125, 137, 145, 149, 157, 173, 181, 185, 193, 197, 229, 233, 241, 257, 265, 269, 277, 281, 293, 313, 317, 325, 337, 349, 353, 365, 373, 389, 397, 401, 409, 421, 425, 433, 445, 449, 457, 461, 481, 485
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Nonsquare integers n for which Pell equation x^2 - n*y^2 = -4 has infinitely many integer solutions. The smallest solutions are given in A078356 and A078357.
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REFERENCES
| O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954, 1957 (Sec. 30, table p. 108).
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MAPLE
| isOddPrim := proc(n::integer) local cf; cf := numtheory[cfrac]((sqrt(n)+1)/2, 'periodic', 'quotients') ; if nops(op(2, cf)) mod 2 =1 then RETURN(true) ; else RETURN(false) ; fi ; end: notA077426 := proc(n::integer) if issqr(n) then RETURN(true) ; elif not isOddPrim(n) then RETURN(true) ; else RETURN(false) ; fi ; end: A077426 := proc(n::integer) local resul, i ; resul := 5 ; i := 1 ; while i < n do resul := resul+4 ; while notA077426(resul) do resul := resul+4 ; od ; i:= i+1 ; od ; RETURN(resul) ; end: for n from 1 to 61 do print(A077426(n)) ; od : - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 25 2006
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CROSSREFS
| A subsequence of A077425.
Odd elements of A003814.
Cf. A077427, A172000.
Sequence in context: A078900 A113482 A191218 * A175768 A002144 A192592
Adjacent sequences: A077423 A077424 A077425 * A077427 A077428 A077429
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KEYWORD
| nonn,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Nov 29 2002
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EXTENSIONS
| Edited and extended by Max Alekseyev (maxale(AT)gmail.com), Mar 03 2010
Edited by Max Alekseyev (maxale(AT)gmail.com), Mar 05 2010
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