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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 (list; graph; refs; listen; history; text; internal format)
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 = 2^7-1 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

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

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Last modified February 4 05:49 EST 2023. Contains 360046 sequences. (Running on oeis4.)