This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A285088 Numbers n such that the number of partitions of n(n+1)/2 (=A000041(A000217(n))) is prime. 3
 2, 3, 8, 3947, 43968, 61681 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Because asymptotically A000041(n*(n+1)/2) ~ exp(Pi*sqrt(2/3*(n*(n+1)/2))) / (4*sqrt(3)*(n*(n+1)/2)), the sum of the prime probabilities ~1/log(A000041(n*(n+1)/2)) is diverging and there are no obvious restrictions on primality; therefore, this sequence may be conjectured to be infinite. 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(3) = 8 is in the sequence because A000041(8*9/2) = 17977 is a prime. PROG (PARI) for(n=1, 2000, if(ispseudoprime(numbpart(n*(n+1)/2)), print1(n, ", "))) CROSSREFS Cf. A000041, A046063, A072213, A284594, A285086, A285087. Sequence in context: A112237 A132502 A113840 * A075849 A005604 A114020 Adjacent sequences:  A285085 A285086 A285087 * A285089 A285090 A285091 KEYWORD nonn,hard,more 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 22 04:39 EDT 2019. Contains 322329 sequences. (Running on oeis4.)