A247856 Decimal expansion of the value of the continued fraction [0; 3, 5, 5, 7, 11, 13, 17, 19, ...] generated by twin primes.
3, 1, 3, 2, 3, 3, 0, 8, 0, 9, 8, 6, 9, 4, 5, 9, 1, 2, 6, 3, 0, 7, 8, 6, 4, 8, 6, 4, 7, 2, 1, 7, 2, 8, 0, 0, 4, 3, 9, 2, 5, 1, 1, 7, 4, 5, 0, 5, 2, 2, 5, 3, 9, 7, 1, 7, 3, 2, 6, 8, 4, 8, 5, 4, 0, 4, 4, 3, 1, 4, 5, 9, 0, 8, 5, 0, 2, 0, 1, 0, 3, 6, 8, 3, 6, 9, 3, 8, 1, 0, 8, 9, 1, 2, 6, 2, 6, 7, 6, 9, 8
Offset: 0
Examples
0.313233080986945912630786486472172800439251174505225397...
Links
- Eric Weisstein's MathWorld, Twin Primes
- Marek Wolf, Continued fractions constructed from prime numbers, arxiv.org/abs/1003.4015, p. 6.
Programs
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Mathematica
twinPrimes = Select[{#, #+2}& /@ Prime[Range[100]], PrimeQ[Last[#]]&] // Flatten; u2 = FromContinuedFraction[Join[{0}, twinPrimes]]; RealDigits[u2, 10, 101] // First