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A105236
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a[n+5]=(a[n+4]*a[n+1]+2*a[n+3]*a[n+2])/a[n].
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0
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1, 1, 1, 1, 1, 3, 5, 11, 41, 233, 689, 5337, 49081, 458299, 3603685, 93208147, 1476087601, 27470407569, 816413467841, 43620306030449, 1172020019840081, 70063780891581107, 5804382690927311525, 511286588817798535899
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| This is a bilinear recurrence of Somos 5 type, hence the terms a[n] are associated with a sequence of points P_n=P_0 + n*P on an elliptic curve E. In this case the curve E has integral j-invariant j=10976.
Primes in this strangely prime-rich sequence include: a(5) = 3, a(6) = 5, a(7)= 11, a(8) = 41, a(12) = 49081, a(9) = 233, a(16) = 1476087601, a(21) = 70063780891581107. - Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 16 2005
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REFERENCES
| A. N. W. Hone, Elliptic curves and quadratic recurrence sequences, Bull. Lond. Math. Soc. 37 (2005) 161-171.
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LINKS
| A. N. W. Hone, Sigma function solution of the initial value problem for Somos 5 sequences.
A. N. W. Hone, Bilinear recurrences and addition formulae for hyperelliptic sigma functions.
A. J. van der Poorten, Elliptic curves and continued fractions, J. Int. Sequences, Volume 8, no. 2 (2005), article 05.2.5.
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CROSSREFS
| Cf. A006721, A006720.
Sequence in context: A174915 A162250 A055511 * A144467 A049883 A059242
Adjacent sequences: A105233 A105234 A105235 * A105237 A105238 A105239
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KEYWORD
| nonn
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AUTHOR
| Andrew N.W. Hone (anwh(AT)kent.ac.uk), Apr 14 2005
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