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A140119
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Extrapolation for (n + 1)-st prime made by fitting least-degree polynomial to first n primes.
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2
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2, 4, 8, 8, 22, -6, 72, -92, 266, -426, 838, -1172, 1432, -398, -3614, 15140, -41274, 95126, -195698, 370876, -652384, 1063442, -1570116, 1961852, -1560168, -1401888, 11023226, -36000318, 93408538, -214275608, 450374202, -879254356, 1599245876, -2695464868, 4138070460, -5539280974
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Construct the least-degree polynomial p(x) which fits the first n primes (p has degree n - 1 or less). Then predict the next prime by evaluating p(n + 1).
a(n) = sum_1_n p_i (-1)^(n - i) binomial(n, i - 1) where p_i are the primes.
Can anything be said about the pattern of positive and negative values?
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LINKS
| Jonathan Wellons, Table of n, a(n) for n = 1..1500
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EXAMPLE
| The lowest-order polynomial having points (1,2), (2,3), (3,5) and (4,7) is f(x) = 1/6 (-x^3 + 9x^2 - 14x + 18). When evaluated at x = 5, f(5) = 8.
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CROSSREFS
| Cf. A140118.
Sequence in context: A132720 A029930 A193850 * A193846 A011402 A131625
Adjacent sequences: A140116 A140117 A140118 * A140120 A140121 A140122
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KEYWORD
| sign
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AUTHOR
| Jonathan Wellons (wellons(AT)gmail.com), May 08, 2008
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