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A208127
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Cardinality of the set f^n({s}), where f is a variant of the Collatz function that replaces any element x in the argument set with both x/2 and 3*x+1, and s is an arbitrary irrational number.
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0
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1, 2, 4, 8, 16, 32, 64, 127, 252, 495, 969, 1886, 3655, 7054, 13562, 25978, 49602, 94440, 179380, 340001, 643276, 1215178, 2292431, 4319603, 8131123, 15292302, 28738320, 53970713, 101297742, 190028125, 356319648, 667866054
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OFFSET
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0,2
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COMMENTS
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The start value can also be chosen as s = i, the imaginary unit.
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LINKS
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Table of n, a(n) for n=0..31.
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FORMULA
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a(n) = |f^n({s})| where f(M) = {x/2 : x in M} union {3x+1 : x in M} and s is an arbitrary irrational number.
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EXAMPLE
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a(7) = 127 = 2^7-1 because there are exactly two 7-length sequences of h:=x->x/2 or t:=x->3*x+1 steps yielding the same value: (hhthtth)(s) = (thhhhtt)(s) = 27/16*s + 7/4. - Alois P. Heinz, Mar 30 2012
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MAPLE
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M := {sqrt(2)}:
print(nops(M)):
for i from 1 to 23 do
M := map(x -> x/2, M) union map(x -> 3*x+1, M):
print(nops(M))
end do:
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CROSSREFS
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Sequence in context: A335247 A145113 A062257 * A172316 A062258 A239560
Adjacent sequences: A208124 A208125 A208126 * A208128 A208129 A208130
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KEYWORD
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nonn,more
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AUTHOR
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Markus Sigg, Mar 29 2012
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EXTENSIONS
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a(23)-a(25) from Alois P. Heinz, Mar 30 2012
a(26)-a(28) from Markus Sigg, Jul 05 2017
a(29)-a(31) from Markus Sigg, Aug 06 2017
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STATUS
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approved
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