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Date: 14-5-2020
838
Date: 1-9-2020
487
Date: 19-11-2020
916
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The continued fraction for is given by [1; 2, 4, 1, 1, 1, 3, 1, 1, 1, 2, 47, 2, ...] (OEIS A099803).
The positions at which the numbers 1, 2, ... occur in the continued fraction are 0, 1, 6, 2, 47, 28, 21, 107, 114, ... (OEIS A000000).
The high-water marks are 1, 2, 4, 47, 99, 294, 527, 616, 1152, ... (OEIS A099804), which occur at positions 0, 1, 2, 11, 69, 125, 201, 584, 1591, 2435, ... (OEIS A229230).
Let the continued fraction of be denoted and let the denominators of the convergents be denoted , , ..., . Then plots above show successive values of , , , which appear to converge to Khinchin's constant (left figure) and , which appear to converge to the Lévy constant (right figure), although neither of these limits has been rigorously established.
REFERENCES:
Sloane, N. J. A. Sequences A099803, A099804, and A229230 in "The On-Line Encyclopedia of Integer Sequences."
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علامات بسيطة في جسدك قد تنذر بمرض "قاتل"
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أول صور ثلاثية الأبعاد للغدة الزعترية البشرية
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مكتبة أمّ البنين النسويّة تصدر العدد 212 من مجلّة رياض الزهراء (عليها السلام)
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