A271973 Smallest number k such that gcd(s1, s2) = n, where s1 is the sum of the odd numbers and s2 is the sum of the even numbers in the Collatz (3x+1) trajectory of k.

1, 10, 9, 30, 65, 5, 74, 86, 368, 135, 970, 50, 95, 101, 1045, 178, 793, 7, 214, 196, 18, 423, 133, 200, 2572, 629, 621, 358, 700, 451, 3167, 1924, 3611, 1926, 662, 510, 6688, 437, 1525, 5072, 3724, 3161, 1034, 240, 5848, 2487, 704, 442, 19120, 1230, 5138, 3524

Offset

1,2

Links

Table of n, a(n) for n=1..52.

Example

a(6) = 5 because the Collatz trajectory of 5 is 5 -> 16 -> 8 -> 4 -> 2 -> 1 with s1 = 5+1 = 6 and s2 = 16+8+4+2 = 30 => gcd(6,30) = 6.

Maple

nn:=10^8:
for n from 1 to 60 do:
ii:=0:
  for k from 1 to nn while(ii=0) do:
   kk:=1:m:=k:T[kk]:=k:it:=0:
    for i from 1 to nn while(m<>1) do:
     if irem(m, 2)=0
      then
       m:=m/2:kk:=kk+1:T[kk]:=m:
      else
      m:=3*m+1:kk:=kk+1:T[kk]:=m:
     fi:
    od:
     s1:=0:s2:=0:
      for j from 1 to kk do:
       if irem(T[j], 2)=1
        then
        s1:=s1+T[j]:
        else
        s2:=s2+T[j]:
       fi:
      od:
       g:=gcd(s1, s2):
       if g=n
       then
       ii:=1:printf("%d %d \n", n, k):
       else fi:
    od:
   od:

Mathematica

Table[k = 1; While[n != GCD[Total@ Select[#, OddQ], Total@ Select[#, EvenQ]] &@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, k, # > 1 &], k++]; k, {n, 52}] (* Michael De Vlieger, Jul 13 2016 *)

Crossrefs

Cf. A213909, A213916.

Sequence in context: A003568 A305196 A099642 * A237114 A217412 A241285

Adjacent sequences: A271970 A271971 A271972 * A271974 A271975 A271976

Keyword

nonn

Author

Michel Lagneau, Jul 13 2016

Status

approved