Does the OEIS have a mode that lets you display the numbers in a different base? That might bring out some patterns that are not visible from the default decimal presentation of entries. I looked at the homepage and the Welcome page but didn’t see anything relevant. (Of course, it is trivial to copy and paste sequences into an application that can handle base conversion.) While we’re talking nonstandard modes of presentation of numbers: Have any mathematical discoveries been triggered by the graphical or auditory presentations of OEIS sequences? Jim Propp On Monday, June 4, 2018, Hans Havermann <gladhobo@bell.net> wrote:
Keith: "One possibility is that in those cases y^x is much greater than x^y and y is divisible by 10."
Indeed, your examples of the 30th and 37th Leyland primes are (x,y) = (357,20) and (471,20) while the 18th and 34th Leyland primes, (81,80) and (237,200), do not exhibit the long string of zeros.
I recently conjectured that for d > 11, 10^(d-1) + (d-1)^10 is the smallest (base ten) d-digit Leyland number. After a bit these will exhibit a long string of zeros after the initial 1. Alas, no primes with y = 10 are yet known.
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