A349646 -id:A349646 - cp's OEIS frontend

A349647 Nonnegative integers which produce a record minimum MD5 hash.

0, 1, 4, 6, 27, 134, 138, 168, 363, 1970, 5329, 738639, 752491, 848775, 1803305, 2420500, 20412333, 207691249, 220455692, 517921150, 521602912, 1149023650, 1289986143, 5963709738, 6262635619, 23831964366, 79255202271, 1970864394858, 2255739204027

Offset: 1

Ben Whitmore, Nov 23 2021

a(1) = 0; a(n) is the smallest k such that MD5(k) < MD5(a(n-1)), where integer parameters to MD5 are encoded as base-10 ASCII strings.
If we assume that MD5 behaves like a random function from N to {0, ..., 2^128-1}, the expected length of this sequence is the harmonic number H(2^128) ~= 89.3.
a(33) > 10^15.

			a(5) = 27 because MD5("27") = 02e74f10e0327ad868d138f2b4fdd6f0_16 = 3859480213286334249913589638377625328, which is smaller than all previous values MD5("0"), ..., MD5("26").

Ben Whitmore, Table of n, a(n) for n = 1..32
Wikipedia, MD5

Record maxima: A349646.

recordsBy[l_, P_] :=
Module[{max = -Infinity, x, i, recs = {}},
For[i = 1, i <= Length[l], i++,
  x = P[l[[i]]];
  If[x > max,
   max = x;
   AppendTo[recs, l[[i]]];
  ]
];
recs
];
recordsBy[Range[1000], -Hash[ToString[#], "MD5"] &]

from hashlib import md5
def afind(limit):
    record = "~"
    for k in range(limit+1):
        hash = md5(str(k).encode('utf-8')).hexdigest()
        if hash < record:
            print(k, end=", ")
            record = hash
afind(10**7) # Michael S. Branicky, Nov 24 2021

cp's OEIS Frontend

A349647 Nonnegative integers which produce a record minimum MD5 hash.

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