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

102987336249554097029535212322581322789799900648198034993379397001115665086549, 85627803894273957621009139791088467240572419248799306945317937552975942820725, 84071438648566403273885734069370854758478523414599514048347910236850479717025, 91949452561369181223012808967964775320445203057864513807052896586217122700773

Offset

1,1

Comments

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.

Links

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

Example

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.

Prog

(Python) # See links
(Python)
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

Crossrefs

Cf. A007931, A076478, A365749, A366061.

Sequence in context: A008868 A095544 A095546 * A095548 A141756 A155538

Adjacent sequences: A378625 A378626 A378627 * A378629 A378630 A378631

Keyword

nonn

Author

David Rabahy, Dec 02 2024

Status

approved