This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A140118 Extrapolation for (n + 1)-st odd prime made by fitting least-degree polynomial to first n odd primes. 3
 3, 7, 9, 19, 3, 49, -39, 151, -189, 381, -371, 219, 991, -4059, 11473, -26193, 53791, -100639, 175107, -281581, 410979, -506757, 391647, 401587, -2962157, 9621235, -24977199, 57408111, -120867183, 236098467, -428880285, 719991383, -1096219131, 1442605443, -1401210665, 99178397, 4340546667 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Construct the least-degree polynomial p(x) which fits the first n odd 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? How many of these terms are the correct (n + 1)th prime? How many terms are prime? The terms at indices 1, 2, 4, 5, 8, 13, 17, 20, 24, 32, 54, 75, 105, 283, 676, 769, 1205 and 1300 actually are prime (ignoring negative signs). LINKS Jonathan Wellons, Table of n, a(n) for n = 1..1500 Jonathan Wellons, Home Page. EXAMPLE The lowest-order polynomial having points (1,3), (2,5), (3,7) and (4,11) is f(x) = 1/3 (x^3 - 6x^2 + 17x - 3). When evaluated at x = 5, f(5) = 19. CROSSREFS Cf. A140119. Sequence in context: A036976 A230116 A031273 * A191106 A324699 A110674 Adjacent sequences:  A140115 A140116 A140117 * A140119 A140120 A140121 KEYWORD sign AUTHOR Jonathan Wellons (wellons(AT)gmail.com), May 08 2008, May 19 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 16 03:37 EDT 2019. Contains 328040 sequences. (Running on oeis4.)