A349647 - OEIS

%I #24 Dec 25 2021 11:16:54

%S 0,1,4,6,27,134,138,168,363,1970,5329,738639,752491,848775,1803305,

%T 2420500,20412333,207691249,220455692,517921150,521602912,1149023650,

%U 1289986143,5963709738,6262635619,23831964366,79255202271,1970864394858,2255739204027

%N Nonnegative integers which produce a record minimum MD5 hash.

%C 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.

%C 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.

%C a(33) > 10^15.

%H Ben Whitmore, <a href="/A349647/b349647.txt">Table of n, a(n) for n = 1..32</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/MD5">MD5</a>

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

%t recordsBy[l_, P_] :=

%t Module[{max = -Infinity, x, i, recs = {}},

%t For[i = 1, i <= Length[l], i++,

%t   x = P[l[[i]]];

%t   If[x > max,

%t    max = x;

%t    AppendTo[recs, l[[i]]];

%t   ]

%t ];

%t recs

%t ];

%t recordsBy[Range[1000], -Hash[ToString[#], "MD5"] &]

%o (Python)

%o from hashlib import md5

%o def afind(limit):

%o     record = "~"

%o     for k in range(limit+1):

%o         hash = md5(str(k).encode('utf-8')).hexdigest()

%o         if hash < record:

%o             print(k, end=", ")

%o             record = hash

%o afind(10**7) # _Michael S. Branicky_, Nov 24 2021

%Y Record maxima: A349646.

%K nonn,base,fini,hard

%O 1,3

%A _Ben Whitmore_, Nov 23 2021