%I #19 Oct 01 2023 09:53:17
%S 1,2,6,7,36,674,815,11621,449652,2386324,2643745,187894152,704719562,
%T 1390873253,1625785299,3479964180,6909167935,12446961112
%N Numbers of iterations that produce a record low of the digest of the SHA2-256 hash of the empty string.
%C The SHA2-256 algorithm takes inputs of any length but here we are feeding the output of every iteration to the next.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/SHA-2">SHA-2</a>.
%e a(1) = 1 because 1 iteration sha256("") = hex e3b0...b855 is taken as the first digest and so is a record.
%e a(2) = 2 is the next term since 2 times nested sha256(...(sha256("")...)) = hex 5df6...9456 is less than the previous record e3b0...b855.
%o (Python)
%o from itertools import islice
%o import hashlib
%o def g():
%o c, vmin, m = 1, b"\xFF" * 32, b""
%o while True:
%o if (m:= hashlib.sha256(m).digest()) < vmin:
%o vmin = m
%o yield c
%o c += 1
%o print(list(islice(g(), 16)))
%Y Cf. A365749.
%K nonn,more,hard,fini,base
%O 1,2
%A _DarĂo Clavijo_, Sep 27 2023
%E a(17)-a(18) from _Michael S. Branicky_, Sep 28 2023