The OEIS is looking to hire part-time people to help edit core sequences, upload scanned documents, process citations, fix broken links, etc. - Neil Sloane, njasloane@gmail.com
Reinhard Zumkeller conjectures (at A102730) that this sequence is finite. I conjecture the contrary, that a(n) exists for every n. Further, I expect a(n) << n^n. [Charles R Greathouse IV, Aug 21 2011]