This site is supported by donations to The OEIS Foundation. Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A065876 a(n) is the smallest m > n such that n^2 + 1 divides m^2 + 1. 7
 1, 3, 3, 7, 13, 21, 31, 43, 18, 73, 91, 111, 17, 47, 183, 211, 241, 133, 57, 343, 381, 47, 172, 83, 553, 601, 651, 173, 342, 813, 242, 265, 132, 403, 411, 1191, 1261, 237, 327, 1483, 1561, 1641, 748, 857, 850, 1981, 684, 463, 413, 2353, 255, 2551, 593, 1177, 2863, 123, 3081, 307, 1288, 3423 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) exists because n^2 + 1 divides (n^2 - n + 1)^2 + 1. The set of n such a(n) = n^2 - n + 1 is S = (2, 3, 4, 5, 6, 7, 9, 11, 14, 15, ...). a(n) = n^2 - n + 1 whenever n^2 + 1 is prime or twice a prime. Up to n=1000, the only other n for which a(n) = n^2 - n + 1 are 7, 41 and 239. Is it a coincidence that these are NSW primes (A088165)? - Franklin T. Adams-Watters, Oct 17 2006 It appears that the density of even numbers in this sequence approaches a limit near 1/4. It appears that the density of even values for indices where a(n) != n^2 - n + 1 is approaching a number near 1/4 and based on the previous comment the density of n for which a(n) = n^2 - n + 1 is almost certainly 0. - Franklin T. Adams-Watters, Oct 17 2006 LINKS Franklin T. Adams-Watters, Table of n, a(n) for n = 0..1000 MATHEMATICA Do[k = 1; While[m = (k^2 + 1)/(n^2 + 1); m < 2 || !IntegerQ[m], k++ ]; Print[k], {n, 1, 40 } ] PROG (PARI) { for (n=0, 1000, a=n+1; while ((a^2 + 1)%(n^2 + 1) != 0, a++); write("b065876.txt", n, " ", a) ) } \\ Harry J. Smith, Nov 03 2009 CROSSREFS Cf. A002731, A005574, A071557, A088165. Sequence in context: A096188 A187873 A306665 * A204858 A095008 A214825 Adjacent sequences:  A065873 A065874 A065875 * A065877 A065878 A065879 KEYWORD nonn AUTHOR Benoit Cloitre, Dec 07 2001 EXTENSIONS More terms from Robert G. Wilson v, Dec 11 2001 Further terms from Franklin T. Adams-Watters, Oct 17 2006 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 December 8 14:38 EST 2019. Contains 329865 sequences. (Running on oeis4.)