A366061 -id:A366061 - cp's OEIS frontend

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

Darío Clavijo, Sep 17 2023

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

			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.

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

Cf. A234849, A366061.

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)))

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

A378628 SHA-256 hash of binary strings ordered by length then lexicographically, interpreting the bits of the resulting hash as a number in binary.

Original entry on oeis.org

102987336249554097029535212322581322789799900648198034993379397001115665086549, 85627803894273957621009139791088467240572419248799306945317937552975942820725, 84071438648566403273885734069370854758478523414599514048347910236850479717025, 91949452561369181223012808967964775320445203057864513807052896586217122700773

Offset: 1

David Rabahy, Dec 02 2024

nonn

The n-th binary string is the bits of the binary expansion of n after its most significant 1 bit, so beginning from n=1: [empty], 0, 1, 00, 01, 10, 11, 000, 001, 010, ... .
The SHA-256 hash function takes as input a vector of bits, possibly empty, and the resulting hash is 256 bits so that a(n) ranges 0 to 2^256-1 inclusive.
The length of the input bit vector is part of the hash, so initial 0 bits will, in general, result in a different hash.

			For n = 1, there are no bits after the most significant 1 bit, so a(1) is the SHA-256 hash of the empty string.
For n = 6 = 110_2, the bits after the most significant 1 are 10, so a(5) is the SHA-256 hash of the bits 10.

David Rabahy, Table of n, a(n) for n = 1..1000
David Rabahy, Python program
NIST, Secure Hash Standard (SHS), FIPS PUB 180-4.
Wikipedia, SHA-2

Cf. A007931, A076478, A365749, A366061.

Python
```
# See links
```

from sha256bit import Sha256bit
def a(n):
    s = bin(n)[3:]
    t = bytearray(int(s[i*8:i*8+8].ljust(8, "0"), 2) for i in range((len(s)+7)//8)) if n > 1 else ""
    return int(Sha256bit(t, bitlen=len(s)).hexdigest(), 16)
print([a(n) for n in range(1, 5)]) # Michael S. Branicky, Dec 08 2024

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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.

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A378628 SHA-256 hash of binary strings ordered by length then lexicographically, interpreting the bits of the resulting hash as a number in binary.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Python

Python