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A088442
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A linear version of the Josephus problem.
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9
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1, 3, 1, 3, 9, 11, 9, 11, 1, 3, 1, 3, 9, 11, 9, 11, 33, 35, 33, 35, 41, 43, 41, 43, 33, 35, 33, 35, 41, 43, 41, 43, 1, 3, 1, 3, 9, 11, 9, 11, 1, 3, 1, 3, 9, 11, 9, 11, 33, 35, 33, 35, 41, 43, 41, 43, 33, 35, 33, 35, 41, 43, 41, 43, 129, 131, 129, 131, 137, 139, 137, 139, 129, 131
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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To get a(n), write 2n+1 as Sum b_j 2^j, then a(n) = 1 + Sum_{j odd} b_j 2^j.
Equals A004514(n) + 1. - Chris Groer (cgroer(AT)math.uga.edu), Nov 10 2003
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EXAMPLE
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If n=4, 2n+1 = 9 = 1 + 0*2 + 0*2^2 + 1*2^3, so a(4) = 1 + 0*2 + 1*2^3 = 9.
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MAPLE
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a:=proc(n) local b: b:=convert(2*n+1, base, 2): 1+sum(b[2*j]*2^(2*j-1), j=1..nops(b)/2) end: seq(a(n), n=0..100);
with(Bits): seq(And(2*n+1, convert("aaaaaa", decimal, hex)) + 1, n=0..127); # Georg Fischer, Dec 03 2022
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MATHEMATICA
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PROG
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(Haskell)
(Magma)
if n le 1 then return n;
else return 4*A063694(Floor(n/4)) + (n mod 2);
end function;
(SageMath)
if (n<2): return n
else: return 4*A063694(floor(n/4)) + (n%2)
(Python)
def A088442(n): return ((n&((1<<(m:=n.bit_length())+(m&1))-1)//3)<<1)+1 # Chai Wah Wu, Jan 30 2023
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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