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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
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OFFSET
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1,2
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COMMENTS
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LINKS
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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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MATHEMATICA
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Convergents[ Array[ 2^IntegerExponent[#, 2]&, 30] ] // Numerator (* Jean-François Alcover, May 15 2014 *)
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PROG
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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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KEYWORD
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cofr,nonn
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AUTHOR
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STATUS
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approved
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