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A361943
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a(n) is the least multiple of n whose binary expansion is an abelian square (A272653).
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1
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3, 10, 3, 36, 10, 36, 63, 136, 9, 10, 33, 36, 130, 154, 15, 528, 34, 36, 190, 520, 63, 132, 46, 528, 150, 130, 54, 588, 725, 150, 1023, 2080, 33, 34, 630, 36, 222, 190, 156, 520, 615, 588, 43, 132, 45, 46, 235, 528, 147, 150, 51, 156, 53, 54, 165, 2296, 513
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OFFSET
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1,1
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COMMENTS
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This sequence is well defined as for any n > 0, A020330(n) is a multiple of n and its binary expansion is an abelian square.
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LINKS
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FORMULA
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a(n) >= n with equality iff n belongs to A272653.
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EXAMPLE
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The first terms, alongside their binary expansion, are:
n a(n) bin(a(n))
-- ---- ----------
1 3 11
2 10 1010
3 3 11
4 36 100100
5 10 1010
6 36 100100
7 63 111111
8 136 10001000
9 9 1001
10 10 1010
11 33 100001
12 36 100100
13 130 10000010
14 154 10011010
15 15 1111
16 528 1000010000
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PROG
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(PARI) a(n) = { forstep (m = n, oo, n, my (w = #binary(m)); if (w%2==0 && hammingweight(m)==2*hammingweight(m % (2^(w/2))), return (m))) }
(Python)
from itertools import count
def a(n): return next(m for m in count(n, n) if not (w:=m.bit_length())&1 and m.bit_count() == ((m>>(w>>1)).bit_count())<<1)
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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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