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 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

%I #12 Sep 12 2017 21:31:47

%S 1,10,9,30,65,5,74,86,368,135,970,50,95,101,1045,178,793,7,214,196,18,

%T 423,133,200,2572,629,621,358,700,451,3167,1924,3611,1926,662,510,

%U 6688,437,1525,5072,3724,3161,1034,240,5848,2487,704,442,19120,1230,5138,3524

%N 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.

%e 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.

%p nn:=10^8:

%p for n from 1 to 60 do:

%p ii:=0:

%p for k from 1 to nn while(ii=0) do:

%p kk:=1:m:=k:T[kk]:=k:it:=0:

%p for i from 1 to nn while(m<>1) do:

%p if irem(m,2)=0

%p then

%p m:=m/2:kk:=kk+1:T[kk]:=m:

%p else

%p m:=3*m+1:kk:=kk+1:T[kk]:=m:

%p fi:

%p od:

%p s1:=0:s2:=0:

%p for j from 1 to kk do:

%p if irem(T[j],2)=1

%p then

%p s1:=s1+T[j]:

%p else

%p s2:=s2+T[j]:

%p fi:

%p od:

%p g:=gcd(s1,s2):

%p if g=n

%p then

%p ii:=1:printf("%d %d \n",n,k):

%p else fi:

%p od:

%p od:

%t 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 *)

%Y Cf. A213909, A213916.

%K nonn

%O 1,2

%A _Michel Lagneau_, Jul 13 2016

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Last modified February 28 21:38 EST 2024. Contains 370400 sequences. (Running on oeis4.)