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

1,1

Comments

This is A091066 with some terms of A020330 removed.

Links

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

Wikipedia, Sesquipower

Example

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

Prog

(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

Crossrefs

Cf. A020330, A091066, A254128, A262312.

Sequence in context: A106505 A097985 A362570 * A099047 A174392 A084926

Adjacent sequences: A342375 A342376 A342377 * A342379 A342380 A342381

Keyword

nonn,base

Author

Peter Kagey, Mar 09 2021

Status

approved