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Search: id:A100340
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| A100340 |
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Numerators of the convergents in the continued fraction expansion for the constant given by A100338, where the partial quotients equal A006519 (greatest power of 2 dividing n). |
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4
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| 1, 3, 4, 19, 23, 65, 88, 769, 857, 2483, 3340, 15843, 19183, 54209, 73392, 1228481, 1301873, 3832227, 5134100, 24368627, 29502727, 83374081, 112876808, 986388545, 1099265353, 3184919251, 4284184604, 20321657667, 24605842271, 69533342209
(list; graph; listen)
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OFFSET
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1,2
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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) = 1, a(2) = 3, a(n) = a(n-1)*A006519(n) + a(n-2).
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EXAMPLE
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The constant is x=1.353871128429882374388894084016608124227333416812...
contfrac(x) = [1;2,1,4,1,2,1,8,1,2,1,4,1,2,1,16,...A006519(n),... ].
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PROGRAM
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(PARI) a(n)=if(n==1, 1, if(n==2, 3, a(n-1)*2^valuation(n, 2)+a(n-2)))
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CROSSREFS
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Cf. A100338, A006519, A100341, A100342, A100343.
Adjacent sequences: A100337 A100338 A100339 this_sequence A100341 A100342 A100343
Sequence in context: A025113 A089427 A020344 this_sequence A042175 A041703 A036253
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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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