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

Author

Darío Clavijo, Sep 17 2023

Keywords

• nonn
• hard
• base
• more
• fini

Comments

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

Examples

			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.
		

Links

• Jeffrey Walton et al., SHA2-256 implementation, Github.
• Wikipedia, SHA-2

Crossrefs

Cf. A234849, A366061.

Programs

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)))

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