This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A285086 Numbers n such that the number of partitions of n^2+1 (=A000041(n^2+1)) is prime. 3
 1, 2, 3914 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Because asymptotically A000041(n^2+1) ~ exp(Pi*sqrt(2/3*(n^2+1))) / (4*sqrt(3)*(n^2+1)), the sum of the prime probabilities ~ 1/log(A000041(n^2+1)) is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite. a(4) > 90000. LINKS Chris K. Caldwell, Top twenty prime partition numbers, The Prime Pages. Eric Weisstein's World of Mathematics, Partition Function P Eric Weisstein's World of Mathematics, Integer Sequence Primes EXAMPLE a(2) = 2 is in the sequence because A000041(2^2+1) = 7 is a prime. PROG (PARI) for(n=1, 3920, if(ispseudoprime(numbpart(n^2+1)), print1(n, ", "))) CROSSREFS Cf. A000041, A046063, A072213, A284594, A285087, A285088. Sequence in context: A065671 A094211 A114573 * A024035 A048831 A114722 Adjacent sequences:  A285083 A285084 A285085 * A285087 A285088 A285089 KEYWORD nonn,hard,more,bref AUTHOR Serge Batalov, Apr 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 23 09:35 EDT 2019. Contains 322385 sequences. (Running on oeis4.)