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A357758 Numbers k such that in the binary expansion of k, the Hamming weight of each block differs by at most 1 from every other block of the same length. 2
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 20, 21, 22, 23, 26, 27, 29, 30, 31, 32, 33, 34, 36, 37, 41, 42, 43, 45, 46, 47, 53, 54, 55, 59, 61, 62, 63, 64, 65, 66, 68, 72, 73, 74, 82, 84, 85, 86, 90, 91, 93, 94, 95, 106, 107, 109, 110, 111 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Leading zeros in binary expansions are ignored.
For any n > 0, there are A005598(n)/2 positive terms with binary length n.
Empirically, if t is a term, then at least one of 2*t or 2*t + 1 is also a term.
If t is a term, then floor(t/2) is also a term.
LINKS
Rémy Sigrist, PARI program
EXAMPLE
For k = 42:
- the binary expansion of 42 is "101010",
- blocks of length 1 have Hamming weight 0 or 1,
- blocks of length 2 have Hamming weight 1,
- blocks of length 3 have Hamming weight 1 or 2,
- blocks of length 4 have Hamming weight 2,
- blocks of length 5 have Hamming weight 2 or 3,
- so 42 belongs to the sequence.
For k = 44:
- the binary expansion of 44 is "101100",
- blocks of length 2 have Hamming weight 0, 1 or 2,
- so 44 does not belong to the sequence.
PROG
(PARI) See Links section.
(Python)
def ok(n):
b = bin(n)[2:]
if "00" in b and "11" in b: return False
for l in range(3, len(b)):
h = set(b[i:i+l].count("1") for i in range(len(b)-l+1))
if max(h) - min(h) > 1: return False
return True
print([k for k in range(112) if ok(k)]) # Michael S. Branicky, Oct 12 2022
CROSSREFS
Sequence in context: A247762 A343268 A107909 * A255724 A285100 A368007
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Oct 12 2022
STATUS
approved

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Last modified March 29 08:53 EDT 2024. Contains 371268 sequences. (Running on oeis4.)