

A208127


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.


0



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

0,2


COMMENTS

The start value can also be chosen as s = i, the imaginary unit.


LINKS

Table of n, a(n) for n=0..31.


FORMULA

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.


EXAMPLE

a(7) = 127 = 2^71 because there are exactly two 7length 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


MAPLE

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:


CROSSREFS

Sequence in context: A335247 A145113 A062257 * A172316 A062258 A239560
Adjacent sequences: A208124 A208125 A208126 * A208128 A208129 A208130


KEYWORD

nonn,more


AUTHOR

Markus Sigg, Mar 29 2012


EXTENSIONS

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


STATUS

approved



