A342378 List of numbers whose binary expansion is an instance of the Zimin pattern ABA.

5, 7, 9, 11, 13, 15, 17, 18, 19, 21, 22, 23, 25, 27, 29, 31, 33, 34, 35, 37, 38, 39, 41, 42, 43, 45, 46, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 85, 86, 87, 89, 90, 91, 93, 94, 95, 97, 99, 101

Offset: 1

Author

Peter Kagey, Mar 09 2021

Keywords

• nonn
• base

Comments

This is A091066 with some terms of A020330 removed.

Examples

			The binary expansion of 182 is 10110110, which is an instance of the pattern ABA with A=10 and B=1101.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..1000
• Wikipedia, Sesquipower

Crossrefs

Cf. A020330, A091066, A254128, A262312.

Programs

Python

def ok(n):
  b = bin(n)[2:]
  for i in range(1, (len(b)+1)//2):
    if b[:i] == b[-i:]: return True
  return False
def aupto(lim): return [m for m in range(lim+1) if ok(m)]
print(aupto(101)) # Michael S. Branicky, Mar 09 2021