A257744 - OEIS

%I #23 Sep 24 2015 18:39:38

%S 1,9,33,135,183,143,95,63,1349,899,1535,1023,4623,7047,18063,14623,

%T 12543,16383,23849,15899,10599,29639,79037,80351,53567,35711,23807,

%U 15871,21161,56429,150477,520929,437979,1167945,863359,1151145,1097595,1392255,1343215

%N Smallest k such that A257743(k)=n.

%C If conjecture in comment in A257743 is true, then the sequence is infinite.

%C For example, if this conjecture is true, then A257743 contains 10^9. Indeed, let n_0 requires N>10^9 times of the map in the name. Then there exists n_1 which requires N-1 times of the map, there exists n_2 which requires N-2 times of the map,..., there exists n_(N-10^9+1) which requires 10^9-1 times of the map such that A257743(n_(N-10^9+1)) = 10^9. Therefore, a(10^9) exists. - _Vladimir Shevelev_, May 15 2015

%H Charles R Greathouse IV, <a href="/A257744/b257744.txt">Table of n, a(n) for n = 1..82</a>

%t oddPart:=#/2^IntegerExponent[#,2]&;

%t a257743=Map[Length[NestWhileList[oddPart[3#+1]&,oddPart[#],!(PrimeQ[#]||#==1)&]]&,Range[10000]];

%t a257744=Flatten[Last[Reap[NestWhile[#+1&,1,!(Sow[Position[a257743,#,1,1]])=={}&]]]] (*_Peter J. C. Moses_, May 07 2015*)

%t (* With function "oddPart" and Range[100000] in "a257743": *)

%t FirstPosition[a257743, #] & /@ Range@ 30 // Flatten (* _Michael De Vlieger_, May 12 2015, Version 10 *)

%o (PARI) stepA257743(n)=n>>=valuation(n, 2); if(isprime(n), 1, n)

%o A257743(n)=my(k=1); while((n=stepA257743(n))>1, n=3*n+1; k++); k

%o v=vector(100); for(n=1,1e9, t=A257743(n); if(t<=#v && v[t]==0, v[t]=n; print("a("t") = "n))) \\ _Charles R Greathouse IV_, May 15 2015

%Y Cf. A257743.

%K nonn

%O 1,2

%A _Vladimir Shevelev_, May 07 2015

%E More terms from _Peter J. C. Moses_, May 07 2015