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

%I A365749 #62 Feb 10 2024 05:58:34
%S A365749 1,13,58,117,216,15752,76392,3129199,10886293,12306717,61545851,
%T A365749 167927267,197150851,212386485,759678443,5902809947,14710854746,
%U A365749 186485968010,335913058990,347769614838,10324357504414,23560859051696,76581364219495
%N A365749 Number of iterations that produce a record high of the digest of the SHA2-256 hash of the empty string.
%C A365749 The SHA2-256 algorithm takes inputs of any length but here we are feeding the output of every iteration to the next.
%H A365749 Jeffrey Walton et al., <a href="https://github.com/noloader/SHA-Intrinsics/tree/master">SHA2-256 implementation</a>, Github.
%H A365749 Wikipedia, <a href="http://en.wikipedia.org/wiki/SHA-2">SHA-2</a>
%e A365749 a(1) = 1 because 1 iteration sha256("") = hex e3b0....b855 is taken as greater than the empty string "" starting point.
%e A365749 a(2) = 13 is the next term since 13 times nested sha256(...(sha256("")...)) = hex f761...8338 is greater than the previous record e3b0....b855.
%o A365749 (Python)
%o A365749 from itertools import islice
%o A365749 import hashlib
%o A365749 def g():
%o A365749   c, vmax, m = 1, b"", b""
%o A365749   while True:
%o A365749     if (m:= hashlib.sha256(m).digest()) > vmax:
%o A365749       vmax = m
%o A365749       yield c
%o A365749     c += 1
%o A365749 print(list(islice(g(),16)))
%Y A365749 Cf. A234849, A366061.
%K A365749 nonn,hard,base,more,fini
%O A365749 1,2
%A A365749 _Darío Clavijo_, Sep 17 2023
%E A365749 a(17) from _Michael S. Branicky_, Sep 27 2023
%E A365749 a(18)-a(20) from _Martin Ehrenstein_, Dec 26 2023
%E A365749 a(21)-a(22) from _Martin Ehrenstein_, Jan 15 2024
%E A365749 a(23) from _Martin Ehrenstein_, Feb 09 2024