A302338 - OEIS

%I #44 Sep 08 2022 08:46:21

%S 4,8,10,16,16,20,22,32,28,32,34,40,40,44,46,64,52,56,58,64,64,68,70,

%T 80,76,80,82,88,88,92,94,128,100,104,106,112,112,116,118,128,124,128,

%U 130,136,136,140,142,160,148,152,154,160,160,164,166,176,172,176,178

%N a(n) = 3*n + 2^v(n) where v(n) denotes the 2-adic valuation of n.

%C The sequence can be seen as a variant of the Collatz map (A006370) where we perform only tripling steps.

%C If the 3x+1 (or Collatz) conjecture is true, then for any n > 0, A006667(n) is the least k such that a^k(n) is a power of two (where a^k denotes the k-th iterate of the sequence).

%H Robert Israel, <a href="/A302338/b302338.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%F a(n) = 3*n + 2^A007814(n).

%F a(2*n) = 2*a(n).

%F a(2*k + 1) = A006370(2*k + 1) for any k >= 0.

%e a(42) = 3*42 + 2^1 = 128.

%p seq(3*n+2^padic:-ordp(n,2), n=1..100); # _Robert Israel_, Apr 29 2018

%t Table[3 n + 2^IntegerExponent[n, 2], {n, 60}] (* _Vincenzo Librandi_, Apr 29 2018 *)

%o (PARI) a(n) = 3*n + 2^valuation(n, 2)

%o (Magma) [3*n+2^Valuation(n, 2): n in [1..60]]; // _Vincenzo Librandi_, Apr 29 2018

%Y Cf. A006370, A006667, A007814.

%K nonn,easy

%O 1,1

%A _Rémy Sigrist_, Apr 28 2018