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A067872 Least m>0 for which m*n^2 + 1 is a square. 6
3, 2, 7, 3, 23, 8, 47, 15, 79, 24, 119, 2, 167, 48, 3, 63, 287, 80, 359, 6, 88, 120, 527, 28, 623, 168, 727, 12, 839, 44, 959, 255, 216, 288, 8, 20, 1367, 360, 19, 77, 1679, 22, 1847, 30, 208, 528, 2207, 7, 2399, 624, 128, 42, 2807, 728, 696, 3, 160, 840, 3479, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Least m>0 for which x^2 - m*y^2 = 1 has a solution with y = n.

For n > 1, a(n) <= n^2-2. - Chai Wah Wu, Jan 26 2016

LINKS

T. D. Noe and Chai Wah Wu, Table of n, a(n) for n = 1..10000 n=1..500 from T. D. Noe

FORMULA

For n a power of an odd prime, a(n)=n^2-2. For n twice a power of an odd prime, a(n)=(n/2)^2-1. - T. D. Noe, Sep 13 2007

EXAMPLE

a(4)=3, based on 3*4^2 + 1 = 7^2.

MATHEMATICA

a[n_] := For[m=1, True, m++, If[IntegerQ[Sqrt[m*n^2+1]], Return[m]]]; Table[a[n], {n, 100}]

lm[n_]:=Module[{m=1}, While[!IntegerQ[Sqrt[m n^2+1]], m++]; m]; Array[lm, 60] (* Harvey P. Dale, Feb 24 2013 *)

PROG

(Haskell)

a067872 n = (until ((== 1) . a010052 . (+ 1)) (+ nn) nn) `div` nn

            where nn = n ^ 2

-- Reinhard Zumkeller, Jun 28 2013

(Python)

def A067872(n):

    y, x, n2 = n*(n+2), 2*n+3, n**2

    m, r = divmod(y, n2)

    while r:

        y += x

        x += 2

        m, r = divmod(y, n2)

    return m # Chai Wah Wu, Jan 25 2016

CROSSREFS

Cf. A033318, A068310.

Cf. A010052.

Sequence in context: A241559 A165794 A075270 * A318457 A198501 A230072

Adjacent sequences:  A067869 A067870 A067871 * A067873 A067874 A067875

KEYWORD

nice,nonn

AUTHOR

Lekraj Beedassy, Feb 25 2002

EXTENSIONS

Edited by Dean Hickerson, Mar 19 2002

STATUS

approved

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)