The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A280717 Given a prime number p, let b = -p and c = p^2. Assuming that the polynomial P(x) := x^2+b*x+c takes at least one prime value for some positive integer x
 3, 7, 43, 1693, 2864557, 8205572225569, 67331415548799635795058613, 4533519519805137360312930667312809111343819483374997, 20552799236454203238557860425684304712780972342513397945121797314302926172950212696842909492430773376197 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The next term is only defined if the set S above is not empty. Conjecture: the sequence is well defined. a(13) has 1654 digits. If S is not empty, then its maximal element is P(x) where x is the least positive integer x <= p/2 such that P(x) is prime. - Chai Wah Wu, Jan 09 2017 LINKS Chai Wah Wu, Table of n, a(n) for n = 1..12 EXAMPLE a(2) = 7, since 7 = max S_3, where S_3 = {x^2-3x+9 : x is an integer with 0 A280717[n - 1]/2 && ! PrimeQ@P[A280717[n - 1], #] &]]; A280717 /@ Range[5] (* Davin Park, Feb 06 2017 *) PROG (Python) from __future__ import division from sympy import isprime A280717_list, n = [3], 3 for _ in range(10):     for i in range(1, n//2+1):         j = i**2+n*(n-i)         if isprime(j):             n = j             A280717_list.append(n)             break # Chai Wah Wu, Jan 09 2017 CROSSREFS Sequence in context: A143684 A156893 A050639 * A100837 A253576 A328690 Adjacent sequences:  A280714 A280715 A280716 * A280718 A280719 A280720 KEYWORD nonn,more,hard AUTHOR Luis H. Gallardo, Jan 07 2017 EXTENSIONS a(5) corrected and a(6)-a(9) added by Chai Wah Wu, Jan 09 2017 STATUS approved

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

Last modified May 20 17:47 EDT 2022. Contains 353876 sequences. (Running on oeis4.)