The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Markus Sigg, Table of n, a(n) for n = 0..42 Markus Sigg, C program to calculate as many terms as possible with given amount of memory. 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 Adjacent sequences: A208124 A208125 A208126 * A208128 A208129 A208130 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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