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A131916
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Continued fraction expansion of 1 / (1 - gamma - ln(2^0.5)) - 12, where gamnma is the Euler-Mascheroni constant.
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3
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1, 8, 4, 2, 1, 5, 1, 1, 5, 1, 1, 3, 8, 1, 4, 2, 6, 9, 5, 97, 2, 1, 1, 2, 9, 8, 5, 3, 16, 1, 31, 2, 1, 8, 7, 1, 2, 1, 15, 1, 1, 1, 3, 1, 12, 3, 11, 2, 1, 1, 13, 1, 3, 6, 1, 15, 9, 3, 4, 1, 2, 1, 5, 1, 1, 1, 18, 2, 5, 8, 1, 3, 1, 1, 2, 3, 12, 1, 8, 1, 2, 1, 1, 1, 2, 17, 13, 3, 1, 1, 1, 5, 1, 1, 3, 2, 1, 2, 3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Decimal expansion is A131915.
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LINKS
| Mark B. Villarino, Ramanujan's Harmonic Number Expansion into Negative Powers of a Triangular Number. Constant occurs in Theorem 6, formula (1.13), page 6.
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FORMULA
| Martin Fuller corrected a typo in the cited paper. It should be: ((12 * gamma) - 11 + (12 * ln(2^0.5))) / (1 - gamma - ln(2^0.5)) or more simply: 1 / (1 - gamma - ln(2^0.5)) - 12.
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EXAMPLE
| 1.1215093407... = 1 + 1/8+ 1/4+ 1/2+ 1/1+ 1/5+ 1/1+ 1/1+ 1/5+ 1/1+ 1/1+ 1/3+ 1/8+ 1/1+ 1/4+ 1/2+ 1/6+ 1/9+ 1/5+ 1/97+ 1/2+ 1/1+ 1/1+ 1/2+ 1/9+ 1/8+ 1/5+ 1/3+ 1/16+ 1/1+ 1/31+ 1/2+ 1/1+ 1/8+ 1/7+ 1/1+ 1/2+ 1/1+ 1/15+ 1/1+ 1/1+ 1/1+ 1/3+ 1/1+ 1/12+ 1/3+ 1/11+ 1/2+ 1/1+ 1/1+ 1/13+ 1/1+ 1/3+ 1/6+ 1/1+ 1/15+ 1/9+ 1/3+ 1/4+ 1/1+ 1/2+ 1/1+ 1/5+ 1/1+ 1/1+ 1/1+ 1/18+ 1/2+ 1/5+ 1/8+ 1/1+ 1/3+ 1/1+ 1/1+ 1/2+ 1/3+ 1/12+ 1/1+ 1/8+ 1/1+ 1/2+ 1/1+ 1/1+ 1/1+ 1/2+ 1/17+ 1/13+ 1/3+ 1/1+ 1/1+ 1/1+ 1/5+ 1/1+ 1/1+ 1/3+ 1/2+ 1/1+ 1/2+ 1/3+ 1/5+ . . .
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CROSSREFS
| Cf. A001008, A001620, A131915, A131917, A131918.
Sequence in context: A197477 A133839 A080828 * A131606 A033328 A097529
Adjacent sequences: A131913 A131914 A131915 * A131917 A131918 A131919
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KEYWORD
| cofr,easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), Jul 27 2007
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