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A337349
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To get a(n), take 3*n+1 and divide out any power of 2; then multiply by 3, subtract 1 and divide out any power of 2.
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4
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1, 1, 5, 7, 19, 1, 7, 1, 37, 5, 23, 25, 55, 7, 1, 17, 73, 19, 41, 43, 91, 1, 25, 13, 109, 7, 59, 61, 127, 1, 17, 35, 145, 37, 77, 79, 163, 5, 43, 11, 181, 23, 95, 97, 199, 25, 13, 53, 217, 55, 113, 115, 235, 7, 61, 31, 253, 1, 131, 133, 271, 17, 35, 71, 289, 73, 149
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OFFSET
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0,3
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COMMENTS
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When a(x) is iterated, what are the limit cycles? Are there any besides (1) and (17 -> 19 -> 43 -> 97 -> 109 -> 61)?
Up to 1000000000 every number eventually reaches one of those two cycles. In this range, the longest trajectory starts with n=458788881 and takes 193 steps to reach 1. - Christian Boyer (cboyer(AT)club-internet.fr), Sep 16 2006
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LINKS
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FORMULA
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MAPLE
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local a;
a := 3*n+1;
while modp(a, 2) = 0 do
a := a/2 ;
end do:
a := 3*a-1 ;
while modp(a, 2) = 0 do
a := a/2 ;
end do:
a ;
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MATHEMATICA
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a[n_] := Module[{k = 3n+1}, k = k/2^IntegerExponent[k, 2]; k = 3k-1; k = k/2^IntegerExponent[k, 2]; k];
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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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N. J. A. Sloane, based on email from Dan Asimov (dasimov(AT)earthlink.net), Sep 15 2006
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STATUS
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approved
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