A331961 a(n) is the greatest square number k such that n AND k = k (where AND denotes the bitwise AND operator).

0, 1, 0, 1, 4, 4, 4, 4, 0, 9, 0, 9, 4, 9, 4, 9, 16, 16, 16, 16, 16, 16, 16, 16, 16, 25, 16, 25, 16, 25, 16, 25, 0, 1, 0, 1, 36, 36, 36, 36, 0, 9, 0, 9, 36, 36, 36, 36, 16, 49, 16, 49, 36, 49, 36, 49, 16, 49, 16, 49, 36, 49, 36, 49, 64, 64, 64, 64, 64, 64, 64

Offset

0,5

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Formula

a(n) = 0 iff n belongs to A062880.

a(n^2) = n^2.

Example

The first terms, alongside the binary representations of n and of a(n), are:
  n   a(n)  bin(n)  bin(a(n))
  --  ----  ------  ---------
   0     0       0          0
   1     1       1          1
   2     0      10          0
   3     1      11          1
   4     4     100        100
   5     4     101        100
   6     4     110        100
   7     4     111        100
   8     0    1000          0
   9     9    1001       1001
  10     0    1010          0
  11     9    1011       1001
  12     4    1100        100
  13     9    1101       1001
  14     4    1110        100
  15     9    1111       1001
  16    16   10000      10000

Prog

(PARI) a(n) = forstep (m=sqrtint(n), 0, -1, if (bitand(n, m^2)==m^2, return (m^2)))
(Python)
from math import isqrt
def A331961(n): return next(m for m in (k**2 for k in range(isqrt(n), -1, -1)) if n&m==m) # Chai Wah Wu, Aug 22 2023

Crossrefs

Cf. A062880, A330270.

Sequence in context: A214926 A268368 A274947 * A279406 A171408 A071907

Adjacent sequences: A331958 A331959 A331960 * A331962 A331963 A331964

Keyword

nonn,base

Author

Rémy Sigrist, Feb 02 2020

Status

approved