A247272 Odd numbers n 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

1,1

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 *)

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 *)

Prog

(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++)

Crossrefs

Cf. A008908, A010120.

Sequence in context: A095585 A095571 A095557 * A272023 A286353 A107077

Adjacent sequences: A247269 A247270 A247271 * A247273 A247274 A247275

Keyword

nonn

Author

Derek Orr, Sep 22 2014

Status

approved