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

Author

Michel Lagneau, Jul 13 2016

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A213909, A213916.

Programs

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 *)