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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. 3
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, 1251374689, 2343968788, 4389333758, 8217535290, 15381296139, 28784811039, 53859503664 (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
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:
PROG
(PARI) \\ maxGB is the available RAM memory size; use allocatemem() before start
a208127(maxGB) = {my (n=log(maxGB)/log(2)+21, v=[I]); for (i=0 , n, if(i>0, v=Set(concat(v/2, 3*v+vector(#v, i, 1)))); print1(#v, ", "))};
a208127(16) \\ Hugo Pfoertner, Apr 09 2023
CROSSREFS
Sequence in context: A335247 A145113 A062257 * A172316 A062258 A239560
KEYWORD
nonn
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
a(32) from Markus Sigg, Mar 26 2023
a(33)-a(34) from Hugo Pfoertner, Mar 26 2023
a(35)-a(38) from Markus Sigg, Apr 06 2023
STATUS
approved

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Last modified June 17 18:36 EDT 2024. Contains 373463 sequences. (Running on oeis4.)