# What are the most unusual approximations to constants you found using MMA?

GROUPS:
 I found a new surprising approximation to the MRB constant. That got me wondering what surprising approximations you could come up with using Mathematica. The MRB constant is . m = NSum[(-1)^n*(n^(1/n) - 1), {n, 1, Infinity}, Method -> "AlternatingSigns", WorkingPrecision -> 2000]; Here is an algorithm that gives over 38 digits per iteration using integer coefficients of an average of less than 38 digits.where the p's come from the following.  p[0] = 1; Table[ t[n] = m - Sum[(x^(1/x)*p[x])/(E^(28*Pi*x) - 157329), {x, 1, n}] ; p[n + 1] = IntegerPart[ t[n]/((n + 1)^(1/(n + 1))/(-157329 + E^(28 (n + 1) Pi)))], {n, 0, 50}]; m - Sum[(x^(1/x)*p[x])/(E^(28*Pi*x) - 157329), {x, 1, 50}] ListLinePlot[Table[p[x], {x, 50}]] . This gives 4.432452533270231425156974872295170503055627479703516515309207411311257382068818424053632*10^-1911 andHow about you?