A225124 -id:A225124 - cp's OEIS frontend

A095381 Initial values for 3x+1 trajectories in which the largest term arising in the iteration is a power of 2.

1, 2, 3, 4, 5, 6, 8, 10, 12, 16, 21, 32, 42, 64, 85, 128, 151, 170, 201, 227, 256, 302, 341, 402, 454, 512, 604, 682, 804, 908, 1024, 1365, 2048, 2730, 4096, 5461, 8192, 10922, 14563, 16384, 19417, 21845, 29126, 32768, 38834, 43690, 58252, 65536, 87381

Offset: 1

Labos Elemer, Jun 14 2004

nonn

Clearly the sequence is infinite and a(n) < 2^n. - Charles R Greathouse IV, May 25 2016

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A025586, A087256, A209229, A225124.

// Valid below A006884(47) = 12327829503 on 64-bit machines.
static long is (unsigned long n) {
  unsigned long r = n;
  n >>= __builtin_ctzl(n); // gcc builtin for A007814
  while (n > 1) {
    n = 3*n + 1;
    if (n > r) r = n;
    n >>= __builtin_ctzl(n);
  }
  return !(r & (r-1));
} // Charles R Greathouse IV, May 25 2016

a095381 n = a095381_list !! (n-1)
a095381_list = map (+ 1) $ elemIndices 1 $ map a209229 a025586_list
-- Reinhard Zumkeller, Apr 30 2013

Coll[n_]:=NestWhileList[If[EvenQ[#],#/2,3*#+1] &,n,#>1&];t={};Do[x = Max[Coll[n]];If[IntegerQ[Log[2,x]],AppendTo[t,n]],{n,90000}];t (* Jayanta Basu, Apr 28 2013 *)

is(n)=my(r=n); while(n>2, if(n%2, n=3*n+1; if(n>r, r=n)); n>>=1); r>>valuation(r,2)==1 \\ Charles R Greathouse IV, May 25 2016

A025586(a(n)) = 2^j for some j.

A231610 The least k such that the Collatz (3x+1) iteration of k contains 2^n as the largest power of 2.

Original entry on oeis.org

1, 2, 4, 8, 3, 32, 21, 128, 75, 512, 151, 2048, 1365, 8192, 5461, 32768, 14563, 131072, 87381, 524288, 184111, 2097152, 932067, 8388608, 5592405, 33554432, 13256071, 134217728, 26512143, 536870912, 357913941, 2147483648, 1431655765, 8589934592, 3817748707

Offset: 0

T. D. Noe, Dec 02 2013

nonn

Very similar to A225124, where 2^n is the largest number in the Collatz iteration of A225124(n). The only difference appears to be a(8), which is 75 here and 85 in A225124. The Collatz iteration of 75 is {75, 226, 113, 340, 170, 85, 256, 128, 64, 32, 16, 8, 4, 2, 1}.

			The iteration for 21 is {21, 64, 32, 16, 8, 4, 2, 1}, which shows that 64 = 2^6 is a term. However, 32 is not the first power of two. We have to wait until the iteration for 32, which is {32, 16, 8, 4, 2, 1}, to see 32 = 2^5 as the first power of two.

Cf. A010120, A054646 (similar sequences).
Cf. A135282, A232503 (largest power of 2 in the Collatz iteration of n).
Cf. A225124.

Collatz[n_?OddQ] := 3*n + 1; Collatz[n_?EvenQ] := n/2; nn = 21; t = Table[-1, {nn}]; n = 0; cnt = 0; While[cnt < nn, n++; q = Log[2, NestWhile[Collatz, n, Not[IntegerQ[Log[2, #]]] &]]; If[q < nn && t[[q + 1]] == -1, t[[q + 1]] = n; cnt++]]; t

a(n) = 2^n for odd n.

cp's OEIS Frontend

A095381 Initial values for 3x+1 trajectories in which the largest term arising in the iteration is a power of 2.

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