A349647 -id:A349647 - cp's OEIS frontend

A349646 Nonnegative integers which produce a record maximum MD5 hash.

0, 3, 44, 65, 83, 373, 575, 1126, 12673, 25670, 30268, 30525, 40691, 48240964, 63327632, 298506737, 369490840, 1113434519, 1647703600, 4958115803, 64657664035, 86155378906, 184280298746, 400812644253, 411723964986, 714853066875, 1627993432495, 2607864795784

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 a(1) were defined as 1 instead of 0, the sequence would begin 1, 2, 3, 44, ... and then continue in the same way.
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(31) > 10^15.

			a(5) = 83 because MD5("83") = fe9fc289c3ff0af142b6d3bead98a923_16 = 338453431832254946862081270079334951203, which is larger than all previous values MD5("0"), ..., MD5("82").

Ben Whitmore, Table of n, a(n) for n = 1..30
Wikipedia, MD5

Record minima: A349647.

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**5) # Michael S. Branicky, Nov 24 2021

A366061 Numbers of iterations that produce a record low of the digest of the SHA2-256 hash of the empty string.

Original entry on oeis.org

1, 2, 6, 7, 36, 674, 815, 11621, 449652, 2386324, 2643745, 187894152, 704719562, 1390873253, 1625785299, 3479964180, 6909167935, 12446961112

Offset: 1

Darío Clavijo, Sep 27 2023

The SHA2-256 algorithm takes inputs of any length but here we are feeding the output of every iteration to the next.

			a(1) = 1 because 1 iteration sha256("") = hex e3b0...b855 is taken as the first digest and so is a record.
a(2) = 2 is the next term since 2 times nested sha256(...(sha256("")...)) = hex 5df6...9456 is less than the previous record e3b0...b855.

Wikipedia, SHA-2.

Cf. A365749 (for record highs).

Cf. A349647 (in MD5).

from itertools import islice
import hashlib
def g():
  c, vmin, m = 1, b"\xFF" * 32, b""
  while True:
    if (m:= hashlib.sha256(m).digest()) < vmin:
      vmin = m
      yield c
    c += 1
print(list(islice(g(), 16)))

a(17)-a(18) from Michael S. Branicky, Sep 28 2023

cp's OEIS Frontend

A349646 Nonnegative integers which produce a record maximum MD5 hash.

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