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

%I A331961 #14 Aug 22 2023 14:14:40
%S A331961 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,
%T A331961 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,
%U A331961 49,36,49,16,49,16,49,36,49,36,49,64,64,64,64,64,64,64
%N A331961 a(n) is the greatest square number k such that n AND k = k (where AND denotes the bitwise AND operator).
%H A331961 Rémy Sigrist, <a href="/A331961/b331961.txt">Table of n, a(n) for n = 0..8192</a>
%F A331961 a(n) = 0 iff n belongs to A062880.
%F A331961 a(n^2) = n^2.
%e A331961 The first terms, alongside the binary representations of n and of a(n), are:
%e A331961   n   a(n)  bin(n)  bin(a(n))
%e A331961   --  ----  ------  ---------
%e A331961    0     0       0          0
%e A331961    1     1       1          1
%e A331961    2     0      10          0
%e A331961    3     1      11          1
%e A331961    4     4     100        100
%e A331961    5     4     101        100
%e A331961    6     4     110        100
%e A331961    7     4     111        100
%e A331961    8     0    1000          0
%e A331961    9     9    1001       1001
%e A331961   10     0    1010          0
%e A331961   11     9    1011       1001
%e A331961   12     4    1100        100
%e A331961   13     9    1101       1001
%e A331961   14     4    1110        100
%e A331961   15     9    1111       1001
%e A331961   16    16   10000      10000
%o A331961 (PARI) a(n) = forstep (m=sqrtint(n), 0, -1, if (bitand(n, m^2)==m^2, return (m^2)))
%o A331961 (Python)
%o A331961 from math import isqrt
%o A331961 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
%Y A331961 Cf. A062880, A330270.
%K A331961 nonn,base
%O A331961 0,5
%A A331961 _Rémy Sigrist_, Feb 02 2020