A247272 Odd numbers m containing 256 as the highest power of 2 in their Collatz (3x+1) iteration.

75, 85, 113, 267, 301, 401, 453, 475, 535, 633, 713, 803, 951, 1069, 1205, 1267, 1425, 1427, 1605, 1611, 1689, 1813, 1901, 2141, 2251, 2417, 2533, 2667, 2671, 2811, 2851, 2853, 3001, 3003, 3163, 3213, 3223, 3377, 3379, 3559, 3561, 3751, 3801, 3805, 3819, 3951, 4001, 4007, 4217, 4277

Offset: 1

Author

Derek Orr, Sep 22 2014

Keywords

• nonn

Comments

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

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000 (First 50 from Derek Orr)
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A008908, A010120.

Programs

Mathematica

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 *)

PARI

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