This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A140118 #7 Jul 07 2025 10:44:40
%S A140118 3,7,9,19,3,49,-39,151,-189,381,-371,219,991,-4059,11473,-26193,53791,
%T A140118 -100639,175107,-281581,410979,-506757,391647,401587,-2962157,9621235,
%U A140118 -24977199,57408111,-120867183,236098467,-428880285,719991383,-1096219131,1442605443,-1401210665,99178397,4340546667
%N A140118 Extrapolation for (n + 1)-st odd prime made by fitting least-degree polynomial to first n odd primes.
%C A140118 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 prime(n + 1).
%C A140118 Can anything be said about the pattern of positive and negative values?
%C A140118 How many of these terms are the correct (n + 1)th prime?
%C A140118 How many terms are prime?
%C A140118 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).
%H A140118 Jonathan Wellons, <a href="/A140118/b140118.txt">Table of n, a(n) for n = 1..1500</a>
%F A140118 a(n) = Sum_{i=1..n} prime(i+1)*(-1)^(n-i)*binomial(n, i-1).
%e A140118 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.
%o A140118 (PARI) a(n) = sum(i=1, n, prime(i+1)*(-1)^(n-i)*binomial(n, i-1)); \\ _Michel Marcus_, Jul 07 2025
%Y A140118 Cf. A140119.
%K A140118 sign
%O A140118 1,1
%A A140118 Jonathan Wellons (wellons(AT)gmail.com), May 08 2008, May 19 2008