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

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

Offset: 1

Author

Darío Clavijo, Sep 27 2023

Keywords

• nonn
• more
• hard
• fini
• base

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 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.
		

Links

• Wikipedia, SHA-2.

Crossrefs

Cf. A365749 (for record highs).

Cf. A349647 (in MD5).

Programs

Python

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)))

Extensions

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