A372680 Integers k such that 2^k contains all powers of 2 not exceeding k as substrings.

124, 192, 322, 808, 830, 957, 1757, 4067, 5489, 6616, 6724, 6794, 7065, 7727, 7728, 7736, 8253, 8938, 9438, 9989, 10194, 10195, 10271, 10350, 10389, 10397, 10445, 10475, 10611, 10835, 11107, 11500, 11606, 11758, 11835, 12089, 12304, 12398, 12501, 12548, 12645, 12694, 12695, 12734, 12820

Offset: 1

Author

Bryle Morga, May 10 2024

Keywords

• nonn
• base

Comments

It is unknown whether this sequence contains infinitely many terms.

Examples

			124 is a term; 2^124 = 21267647932558653966460912964485513216 contains 2, 4, 8, 16, 32, 64 as substrings.
		

Crossrefs

Cf. A046300, A094776, A371808.

Programs

Python

def f(m):
  a = str(2**m)
  for i in range(0, m.bit_length()):
    if str(2**i) not in a:
      return 0
  return 1
def a(n):
  m = 0
  i = 0
  while i != n:
    m += 1
    i += f(m)
  return m