A276202 Smallest integer k such that the number of semiprimes in {k, f(k), f(f(k)), ..., 1} is equal to n, where f is the Collatz function.

1, 4, 3, 6, 11, 7, 14, 9, 25, 33, 59, 57, 39, 135, 191, 127, 123, 159, 219, 379, 251, 167, 223, 111, 793, 263, 175, 466, 103, 137, 183, 91, 121, 107, 71, 47, 31, 41, 27, 97, 145, 129, 171, 231, 235, 553, 411, 487, 327, 649, 703, 763, 1519, 1215, 1471, 1071

Offset

0,2

Comments

Smallest k such that A275866(k) is equal to n.

Conjecture: a(n) exists for any n.

Links

Michel Lagneau, Table of n, a(n) for n = 0..100

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

a(5)=7 because the trajectory of 7 is 7 -> 22 -> 11 -> 34 -> 17 -> 52 -> 26 -> 13 -> 40 -> 20 -> 10 -> 5 -> 16 -> 8 -> 4 -> 2 -> 1 and the 5 semiprimes of this trajectory are 22, 34, 26, 10 and 4.

Mathematica

f[n_]:=n/2/; Mod[n, 2]==0; f[n_]:=3 n+1/; Mod[n, 2]==1; g[n_]:=Module[{i, p}, i=n; p=0; While[i>1, If[PrimeOmega[i]==2, p=p+1]; i=f[i]]; p]; Do[k=1; While[g[k]!=m, k++]; Print[m, " ", k], {m, 0, 53}]

Crossrefs

Cf. A006577, A275866.

Sequence in context: A353401 A196889 A005522 * A215336 A328650 A343891

Adjacent sequences: A276199 A276200 A276201 * A276203 A276204 A276205

Keyword

nonn

Author

Michel Lagneau, Aug 29 2016

Status

approved