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Search: id:A100342
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| A100342 |
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Numerators of the convergents in the continued fraction expansion for twice the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n) interleaved with 2's. |
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4
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| 2, 3, 8, 19, 46, 65, 176, 769, 1714, 2483, 6680, 15843, 38366, 54209, 146784, 1228481, 2603746, 3832227, 10268200, 24368627, 59005454, 83374081, 225753616, 986388545, 2198530706, 3184919251, 8568369208, 20321657667, 49211684542
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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The convergents for the continued fraction of x are given by A100340(n)/A100341(n) and the convergents for the continued fraction of 2*x are given by A100342(n)/A100343(n), where A100342(n)/A100343(n) = 2*A100340(n)/A100341(n) for all n.
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FORMULA
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a(1) = 2, a(2) = 3; a(2*n) = a(2*n-1)*A006519(n) + a(2*n-2) for n>1, a(2*n-1) = 2*a(2*n-2) + a(2*n-3) for n>1.
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EXAMPLE
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The constant is 2*x=2.707742256859764748777788168033216248454666833624237..
contfrac(2*x) = [2;1, 2,2, 2,1, 2,4, 2,1, 2,2, 2,1, 2,8,... 2, A006519(n),... ].
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PROGRAM
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(PARI) {a(n)=if(n==1, 2, if(n==2, 3, if(n%2==1, 2*a(n-1)+a(n-2), a(n-1)*2^valuation(n/2, 2)+a(n-2))))}
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CROSSREFS
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Cf. A100338, A006519, A100340, A100341, A100343.
Sequence in context: A041205 A002356 A166302 this_sequence A041281 A078343 A148038
Adjacent sequences: A100339 A100340 A100341 this_sequence A100343 A100344 A100345
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KEYWORD
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cofr,nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Nov 18 2004
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