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

1,3

Comments

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.

Links

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

Wikipedia, MD5

Example

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

Mathematica

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"] &]

Prog

(Python)
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

Crossrefs

Record maxima: A349646.

Sequence in context: A105409 A109934 A068321 * A012896 A013078 A106286

Adjacent sequences: A349644 A349645 A349646 * A349648 A349649 A349650

Keyword

nonn,base,fini,hard

Author

Ben Whitmore, Nov 23 2021

Status

approved