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A191815
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Decimal expansion of the number 1+2/(1+3/(1+5/(1+7/(1+11/(...))))), where the numerators are the primes.
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3
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1, 9, 5, 9, 4, 0, 5, 1, 1, 6, 0, 2, 0, 7, 9, 9, 2, 8, 0, 4, 4, 1, 7, 5, 9, 7, 7, 8, 4, 1, 2, 6, 3, 8, 6, 9, 6, 6, 8, 1, 9, 1, 5, 4, 4, 0, 4, 8, 9, 9, 4, 6, 8, 9, 7, 3, 7, 2, 6, 9, 9, 0, 9, 4, 1, 5, 9, 2, 6, 9, 7, 6, 6, 0, 2, 1
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OFFSET
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1,2
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COMMENTS
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Successive applications of x -> 1+1/x (resp. x -> 1/(1+x)) yield a sequence converging to the Golden ratio (sqrt(5)+1)/2 (resp. (sqrt(5)-1)/2), A001622.
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LINKS
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EXAMPLE
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1.959405116020799280441759778412638696681915440489946897372699094159269766...
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PROG
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(PARI) default(realprecision, 80); s=sqrt(p=1e6); while( p=precprime(p-1), s=p/(1+s)); return(1+s)
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CROSSREFS
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Cf. A191816 for the continued fraction.
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KEYWORD
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AUTHOR
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STATUS
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approved
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