A366061 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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

Wikipedia, SHA-2.

EXAMPLE

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.

PROG

(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)))

CROSSREFS

KEYWORD

nonn,more,hard,fini,base

AUTHOR

EXTENSIONS

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

STATUS

approved