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Search: id:A096995
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| A096995 |
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Number of transient terms if f(x)=sigma(phi(x))=A062402 is iterated at initial value=2^n. |
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5
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| 0, 1, 1, 1, 1, 1, 3, 3, 1, 2, 3, 5, 2, 3, 6, 15, 1, 6, 8, 3, 15, 9, 4, 65, 44, 82, 83, 77, 75, 48, 26, 43, 1
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OFFSET
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0,7
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COMMENT
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For transient lengths of iterations A062401(x) or A096402(x), if started at 2^n, holds that A096994(n)+1 = a(n). Corresponding cycle lengths satisfy A096852(n-1) = A096857(n). Behind these observation several relationships stand, e.g. sigma(A062401(x)) = A062402(sigma(x)) or phi(A062402(x)) = A062401(phi(x)).
For initial value=2^33 more than 38000 iterations did not lead to a recurrent term, so possibly there is no cycle. a(34) through a(39) are 8, 52, 71, 24, 40, 12. - Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 19 2007
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EXAMPLE
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Trajectory of 2^0 is 1,1, ...; there are zero transient terms preceding the 1-cycle (1), so a(0) = 0.
Trajectory of 2^14 is 16384, 16383, 34200, 30480, 26520, 16380, 10200, 6138, 6045, 9906, 9920, 12264, 10200, ...; there are six transient terms preceding the 6-cycle (10200, 6138, 6045, 9906, 9920, 12264), so a(14) = 6.
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CROSSREFS
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Cf. A096402, A062401, A096857, A096852, A096994.
Sequence in context: A107292 A004550 A096836 this_sequence A010264 A089680 A123561
Adjacent sequences: A096992 A096993 A096994 this_sequence A096996 A096997 A096998
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jul 22 2004
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EXTENSIONS
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Edited and corrected by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Jul 19 2007
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