The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A352631 Minimum number of zeros in a binary n-digit perfect square, or -1 if there are no such numbers. 1
0, -1, 2, 2, 2, 3, 2, 4, 3, 4, 3, 4, 4, 5, 2, 5, 4, 6, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 6, 8, 8, 6, 7, 7, 8, 8, 9, 8, 9, 9, 8, 9, 10, 9, 9, 10, 9, 9, 9, 9, 10, 10, 10, 10, 11, 10, 11, 11, 11, 9, 9, 11, 11, 11, 12, 11, 12, 11, 12 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Is there a formula that is easy to compute?
LINKS
EXAMPLE
a(6) = 3, because there are two 6-bit squares 36 = 100100_2 and 49 110001_2 with 4 and 3 zeros, respectively.
a(2) = -1, because the first two perfect squares 1 = 1_2 and 4 = 100_2 have 1 and 3 bits, respectively.
PROG
(Python)
from gmpy2 import is_square, popcount
for n in range(1, 33):
m=n+1
for k in range(2**(n-1), 2**n):
if is_square(k):
m=min(m, n-popcount(k))
print(n, -1 if m>n else m)
(Python 3.10+)
def A352631(n): return -1 if n == 2 else min(n-(k**2).bit_count() for k in range(1+isqrt(2**(n-1)-1), 1+isqrt(2**n))) # Chai Wah Wu, Mar 28 2022
CROSSREFS
Sequence in context: A278636 A126336 A364421 * A134446 A125749 A014085
KEYWORD
sign,base
AUTHOR
Martin Ehrenstein, Mar 25 2022
EXTENSIONS
a(43)-a(71) from Pontus von Brömssen, Mar 26 2022
a(72)-a(80) from Chai Wah Wu, Apr 01 2022
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 23 17:39 EDT 2024. Contains 372765 sequences. (Running on oeis4.)