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Search: id:A164816
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| A164816 |
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Prime factors in a divisibility sequence of the Lucas sequence v(P=3,Q=5) of the second kind. |
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+0
1
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OFFSET
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1,1
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COMMENT
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This is the last sequence on p. 15 of Smyth. The Lucas sequence with P = 3, Q = 5
is defined as v=2,3,-1,-18,-49,-57,.. where v(n) = P*v(n-1)-Q*v(n-2), with g.f. (2-3x)/(1-3x+5x^2).
The indices n such that n|v(n) define the sequence
T = 1,3,9,27,81,153,243,459,... as listed by Smyth.
The OEIS sequence shows all distinct prime factors of elements of T.
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REFERENCES
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Richard Andre-Jeannin, Divisibility of generalized Fibonacci and Lucas numbers by their subscripts, Fibonacci Quart., 29(4) (1991) 364-366.
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LINKS
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Yu. Bilu, G. Hanrot, and P. M. Voutier, Existence of primitive divisors of Lucas and Lehmer numbers, J. Reine Angew. Math., 539 (2001) 75-122.
R. D. Carmichael, On the numerical factors of the arithmetic forms alpha*n+-beta*n, Annals of Math., 2nd ser., 15 (1/4) (1913/14) 30-48.
Chris Smyth, The terms in Lucas sequences divisible by their indices, Aug 28, 2009.
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CROSSREFS
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Sequence in context: A055739 A056794 A135726 this_sequence A042978 A089675 A041383
Adjacent sequences: A164813 A164814 A164815 this_sequence A164817 A164818 A164819
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KEYWORD
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more,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Aug 26 2009
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EXTENSIONS
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More detailed definition, comments rephrased, non-ascii characters in URL's removed - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 09 2009
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