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A331961
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a(n) is the greatest square number k such that n AND k = k (where AND denotes the bitwise AND operator).
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1
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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
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OFFSET
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0,5
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LINKS
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FORMULA
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a(n^2) = n^2.
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EXAMPLE
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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