A366160 Numbers whose binary expansion is not quasiperiodic.

1, 2, 4, 5, 6, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 61, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79

Offset: 1

Author

Darío Clavijo, Oct 02 2023

Keywords

• nonn
• base

Comments

See A320441 for the definition of quasiperiodic.

All numbers 2^k + 1 >= 5 are terms (A000051).

All powers of 2 are terms (A000079).

Crossrefs

Cf. A000051, A000079, A000225, A320441 (complement).

Programs

Python

A000225 = lambda n: (1 << n) - 1
def isA320441(k):
  # Code after Michael S. Branicky, Mar 24 2022 in A320434.
  tt, l = 1, k.bit_length()
  for x in range(0, l + 1):
    m = A000225(x)
    t = k & m
    if (t != tt):
      if (t == k): return False
      r = k
      for g in range(0, x):
        r >>= 1
        if (r & m == t) and (r == t): return True
      tt = t
print([n for n in range(1,80) if not isA320441(n)])