hobbes@namagiri:~/scratch$ echo gYxseNjwafVPfgsoHnzLblmmAxZUiOnGcchqEAEwjyxwjUIfpXfJQcdLapTmFaqHGCFsdvpLarmPJLOZYMEILGNIPwNOgEazuBVJcyVjBRL|ent
    Entropy = 5.352821 bits per byte.
    
    Optimum compression would reduce the size
    of this 108 byte file by 33 percent.
    
    Chi square distribution for 108 samples is 650.52, and randomly
    would exceed this value less than 0.01 percent of the times.
    
    Arithmetic mean value of data bytes is 92.6019 (127.5 = random).
    Monte Carlo value for Pi is 4.000000000 (error 27.32 percent).
    Serial correlation coefficient is 0.142915 (totally uncorrelated = 0.0).
    

...Which is meaningless without context. Let's see if we can create some context...

    hobbes@namagiri:~/scratch$ echo "You have no way of knowing that. All you see are some random-looking strings. These could be numbers (random or not) that were encoded as base52. These could also be numbers encoded as base64, or base88, or any other base52+. Or they could be randomly-generated strings and there is no meaningful number underlying them." |base64 |sed -e :a -e '$!N; s/\n//; ta'
    WW91IGhhdmUgbm8gd2F5IG9mIGtub3dpbmcgdGhhdC4gQWxsIHlvdSBzZWUgYXJlIHNvbWUgcmFuZG9tLWxvb2tpbmcgc3RyaW5ncy4gVGhlc2UgY291bGQgYmUgbnVtYmVycyAocmFuZG9tIG9yIG5vdCkgdGhhdCB3ZXJlIGVuY29kZWQgYXMgYmFzZTUyLiBUaGVzZSBjb3VsZCBhbHNvIGJlIG51bWJlcnMgZW5jb2RlZCBhcyBiYXNlNjQsIG9yIGJhc2U4OCwgb3IgYW55IG90aGVyIGJhc2U1MisuIE9yIHRoZXkgY291bGQgYmUgcmFuZG9tbHktZ2VuZXJhdGVkIHN0cmluZ3MgYW5kIHRoZXJlIGlzIG5vIG1lYW5pbmdmdWwgbnVtYmVyIHVuZGVybHlpbmcgdGhlbS4K

ok, that's base64. Let's turn that into base52...

    CL-USER> (to-base 52 (from-base 64 "WW91IGhhdmUgbm8gd2F5IG9mIGtub3dpbmcgdGhhdC4gQWxsIHlvdSBzZWUgYXJlIHNvbWUgcmFuZG9tLWxvb2tpbmcgc3RyaW5ncy4gVGhlc2UgY291bGQgYmUgbnVtYmVycyAocmFuZG9tIG9yIG5vdCkgdGhhdCB3ZXJlIGVuY29kZWQgYXMgYmFzZTUyLiBUaGVzZSBjb3VsZCBhbHNvIGJlIG51bWJlcnMgZW5jb2RlZCBhcyBiYXNlNjQsIG9yIGJhc2U4OCwgb3IgYW55IG90aGVyIGJhc2U1MisuIE9yIHRoZXkgY291bGQgYmUgcmFuZG9tbHktZ2VuZXJhdGVkIHN0cmluZ3MgYW5kIHRoZXJlIGlzIG5vIG1lYW5pbmdmdWwgbnVtYmVyIHVuZGVybHlpbmcgdGhlbS4K"))
    "6lH81qbtcGjfFOclhdtt7ieuljADG17Ou6swolu2A2qlnO52zmMkG8Nfk2APbEbso4idFF44wsLIGfrOg5atP0ucg5gubxAcD9ztMcboeC4sAui28skbwtEiuv64OuD8fbFnn1M01oeq3bH7n9bvu8p3P1MwirdDHxKDONktDvtNOLE1srOz2I4wNLsBpgOGIlLs1i11xt58JpOC1whJ54Krmln1ahmrvksODe7kqjtBazKzKamu5tygI6hGHq3h123Ighyw8s2MxE4dl9rBdBNG1o7tJM2HvzOh955NpLB33nuPr4OwfhjB618y1BP9y2euMquIMszOuH1rPAEkBccOu9qIJBqKgGf1qH42bBd7GOMsbKExosd8CErJlMIAcEyyytFzoKOfkJy1ExEnKc0iE7OGkpLJM3ybB2JNlnwtrC5F0cH8kB41IIv0BwNk9DO"

Astute readers will note that this output contains numeric digits. There's more than one representation of "base-52". The one above goes from 0 through p. An alternative would go from A-z. But none of that matters to measure the entropy of base-52 encoded English text, ya dig?

    hobbes@namagiri:~/scratch$ echo "6lH81qbtcGjfFOclhdtt7ieuljADG17Ou6swolu2A2qlnO52zmMkG8Nfk2APbEbso4idFF44wsLIGfrOg5atP0ucg5gubxAcD9ztMcboeC4sAui28skbwtEiuv64OuD8fbFnn1M01oeq3bH7n9bvu8p3P1MwirdDHxKDONktDvtNOLE1srOz2I4wNLsBpgOGIlLs1i11xt58JpOC1whJ54Krmln1ahmrvksODe7kqjtBazKzKamu5tygI6hGHq3h123Ighyw8s2MxE4dl9rBdBNG1o7tJM2HvzOh955NpLB33nuPr4OwfhjB618y1BP9y2euMquIMszOuH1rPAEkBccOu9qIJBqKgGf1qH42bBd7GOMsbKExosd8CErJlMIAcEyyytFzoKOfkJy1ExEnKc0iE7OGkpLJM3ybB2JNlnwtrC5F0cH8kB41IIv0BwNk9DO" | ent
    Entropy = 5.610518 bits per byte.
    
    Optimum compression would reduce the size
    of this 452 byte file by 29 percent.
    
    Chi square distribution for 452 samples is 2093.27, and randomly
    would exceed this value less than 0.01 percent of the times.
    
    Arithmetic mean value of data bytes is 86.3496 (127.5 = random).
    Monte Carlo value for Pi is 4.000000000 (error 27.32 percent).
    Serial correlation coefficient is 0.018253 (totally uncorrelated = 0.0).

Conclusion: I don't think the original text was pseudorandom. If you can convince me that the original isn't "base-52 encoded" at all (and I'd be easily convinced), I'm willing to reevaluate that conclusion. I'm also interested to see if anyone sees a flaw in my process.