The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A260389 For the Collatz (3x+1) iteration starting at k, the sequence lists the smallest k such that Fibonacci(n) belongs to the trajectory of k, or 0 if no such k exists. 1
 2, 2, 3, 6, 3, 3, 7, 42, 7, 73, 39, 288, 27, 27, 135, 1974, 1419, 861, 2787, 13530, 7297, 5247, 33963, 92736, 100033, 161857, 116395 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS The initial term k is not counted as an element of the trajectory. LINKS EXAMPLE a(1)=a(2)=2 because 1 = Fibonacci(1)=Fibonacci(2) is in the trajectory 2 -> 1; a(3)=3 because 2 = Fibonacci(3) is in the trajectory 3 -> 10 -> 5 -> ... -> 2 ->1; a(4)=6 because 7 = Fibonacci(4)=3 is in the trajectory 6 -> 3 -> 10 -> ... -> 1; a(5)=3 because 5 = Fibonacci(5)=3 is in the trajectory 3 -> 10 -> 5 -> ... -> 1. a(6)=3 because 8 = Fibonacci(6)=3 is in the trajectory 3 -> 10 -> 5 -> 16 -> 8 -> ... -> 1; a(7)=7 because 13 = Fibonacci(7)=3 is in the trajectory 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> ... -> 1. MAPLE with(numtheory):with(combinat, fibonacci): for n from 1 to 10000 do: jj:=0: for k from 2 to 10^8 while(jj=0) do: lst:={}:m:=k:ii:=0:it:=10^6:    for i from 1 to it while(ii=0) do:     if irem(m, 2)=0     then     m:=m/2:     else m:=3*m+1:     fi:     lst:=lst union {m}:      if m=1      then      ii:=1:      else      fi:    od:     n0:=nops(lst):     for j from 1 to n0 while(jj=0)do:      if fibonacci(n)=lst[j]      then      jj:=1:      else fi:     od:      if jj=1 then printf("%d %d \n", n, k):      else fi:     od:od: CROSSREFS Cf. A000045, A006577. Sequence in context: A284785 A076333 A015051 * A291372 A064426 A051173 Adjacent sequences:  A260386 A260387 A260388 * A260390 A260391 A260392 KEYWORD nonn,hard AUTHOR Michel Lagneau, Nov 22 2015 STATUS approved

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

Last modified May 7 20:36 EDT 2021. Contains 343652 sequences. (Running on oeis4.)