|
Search: id:A140119
|
|
|
| A140119 |
|
Extrapolation for (n + 1)-st prime made by fitting least-degree polynomial to first n primes. |
|
+0
2
|
|
| 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; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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?
|
|
LINKS
|
Jonathan Wellons, Table of n, a(n) for n = 1..1500
|
|
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.
|
|
CROSSREFS
|
Cf. A140118.
Sequence in context: A076735 A132720 A029930 this_sequence A011402 A131625 A044952
Adjacent sequences: A140116 A140117 A140118 this_sequence A140120 A140121 A140122
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Jonathan Wellons (wellons(AT)gmail.com), May 08, 2008
|
|
|
Search completed in 0.003 seconds
|
