A365749 Number of iterations that produce a record high of the digest of the SHA2-256 hash of the empty string.

1, 13, 58, 117, 216, 15752, 76392, 3129199, 10886293, 12306717, 61545851, 167927267, 197150851, 212386485, 759678443, 5902809947, 14710854746, 186485968010, 335913058990, 347769614838, 10324357504414, 23560859051696, 76581364219495

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..23.

Jeffrey Walton et al., SHA2-256 implementation, Github.

Wikipedia, SHA-2

Example

a(1) = 1 because 1 iteration sha256("") = hex e3b0....b855 is taken as greater than the empty string "" starting point.
a(2) = 13 is the next term since 13 times nested sha256(...(sha256("")...)) = hex f761...8338 is greater than the previous record e3b0....b855.

Prog

(Python)
from itertools import islice
import hashlib
def g():
  c, vmax, m = 1, b"", b""
  while True:
    if (m:= hashlib.sha256(m).digest()) > vmax:
      vmax = m
      yield c
    c += 1
print(list(islice(g(), 16)))

Crossrefs

Cf. A234849, A366061.

Sequence in context: A147019 A230988 A183317 * A055833 A103220 A086221

Adjacent sequences: A365746 A365747 A365748 * A365750 A365751 A365752

Keyword

nonn,hard,base,more,fini

Author

Darío Clavijo, Sep 17 2023

Extensions

a(17) from Michael S. Branicky, Sep 27 2023

a(18)-a(20) from Martin Ehrenstein, Dec 26 2023

a(21)-a(22) from Martin Ehrenstein, Jan 15 2024

a(23) from Martin Ehrenstein, Feb 09 2024

Status

approved