A247272 - OEIS

%I #31 Feb 10 2019 20:20:44

%S 75,85,113,267,301,401,453,475,535,633,713,803,951,1069,1205,1267,

%T 1425,1427,1605,1611,1689,1813,1901,2141,2251,2417,2533,2667,2671,

%U 2811,2851,2853,3001,3003,3163,3213,3223,3377,3379,3559,3561,3751,3801,3805,3819,3951,4001,4007,4217,4277

%N Odd numbers n containing 256 as the highest power of 2 in their Collatz (3x+1) iteration.

%C a(n)*2^k also contains 256 as the highest power of 2 for any k >= 0.

%H Harvey P. Dale, <a href="/A247272/b247272.txt">Table of n, a(n) for n = 1..1000</a> (* First 50 from Derek Orr *)

%t hp256Q[n_]:=Max[Select[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&],IntegerQ[ Log[ 2,#]]&]]==256; Select[Range[1,4301,2],hp256Q] (* _Harvey P. Dale_, Feb 10 2019 *)

%o (PARI)

%o Max2(n)=v=[n];while(n!=1,if(n==Mod(0,2),n=n/2;v=concat(v,n));if(n==Mod(1,2)&&n!=1,n=3*n+1;v=concat(v,n)));k=1;while(vecsearch(vecsort(v),2^k),k++);2^(k-1)

%o n=1;while(n<10^4,if(n%2&&Max2(n)==256,print1(n,", "));n++)

%Y Cf. A008908, A010120.

%K nonn

%O 1,1

%A _Derek Orr_, Sep 22 2014