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A153111
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Solutions of the Pell-like equation 1 + 6*A*A = 7*B*B. A,B integers.
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4
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1, 25, 649, 16849, 437425, 11356201, 294823801, 7654062625, 198710804449, 5158826853049, 133930787374825, 3477041644892401, 90269151979827601, 2343520909830625225, 60841274503616428249, 1579529616184196509249
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| B is of the form B(i)= 26*B(i-1) - B(i-2); B(0)=1;B(1)=25 (this sequence). A is of the form A(i)= 26*A(i-1) - A(i-2) ; A(0)=1 ; A(1)=27 . In general a Pell-like equation of the form 1 + X*A*A = (X+1)*B*B has the solution A(i) = (4*X+2)*A(i-1) - A(i-2) ; A(0)=1 ; A(1)=(4*X+3) and B(i) = (4*X+2)*B(i-1) - B(i-2) ; B(0)=1 ; B(1)=(4*X+1) . Examples in OEIS : X=1 gives A002315 for A(i) and A001653 for B(i), X=2 gives A054320 for A(i) and A072256 for B(i), X=3 gives A028230 for A(i) and A001570 for B(i), X=4 gives A049629 for A(i) and A007805 for B(i), X=5 gives A133283 for A(i) and {1,21,461,10121,...} for B(i), X=6 gives {1,27,701,...} for A(i) and this sequence for B(i).
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REFERENCES
| Luigi Cimmino, Algebraic relations for recursive sequences. http://arxiv.org/abs/math/0510417v3
Jeroen Demeyer, Diophantine sets of polynomials over number fields. http://arxiv.org/abs/0807.1970v2
Franz Lemmermeyer, Conics - a Poor Man's Elliptic Curves. http://arxiv.org/abs/math/0311306v1
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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CROSSREFS
| Cf. A002315, A001653, A054320, A072256, A001078, A028230, A001570, A049629, A007805, A133283, A140480,
Sequence in context: A042202 A203341 A152256 * A097194 A180811 A015697
Adjacent sequences: A153108 A153109 A153110 * A153112 A153113 A153114
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KEYWORD
| easy,nonn
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AUTHOR
| Ctibor O. Zizka (c.zizka(AT)email.cz), Dec 18 2008
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EXTENSIONS
| More terms from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2009; corrected by N. J. A. Sloane, Sep 20 2009
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