A165415 a(n) = the smallest positive integer that contains more digits written in binary than n has written in binary, and which does not contain binary n as a substring in its binary representation.

7, 4, 10, 8, 8, 8, 18, 16, 16, 16, 16, 16, 16, 16, 34, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 66, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 64, 130, 128, 128, 128, 128, 128, 128

Offset

2,1

Links

Table of n, a(n) for n=2..70.

Formula

a(2) = 7. For n >=2: a(2^n) = 2^(n+1) + 2; for m such that 2^(n-1)+1 <= m <= 2^n-1, a(m) = 2^n.

Prog

(Python)
def a(n):
    if n == 2: return 7
    digs = n.bit_length()
    return int(2**digs) if n != 2**(digs - 1) else int(2**digs + 2)
print([a(n) for n in range(2, 71)]) # Michael S. Branicky, Jul 04 2021

Crossrefs

Sequence in context: A195452 A103227 A335166 * A069199 A359014 A138339

Adjacent sequences: A165412 A165413 A165414 * A165416 A165417 A165418

Keyword

base,easy,nonn

Author

Leroy Quet, Sep 17 2009

Extensions

Extended by Ray Chandler, Mar 13 2010

Status

approved