A075482 - OEIS

%I #20 Oct 09 2018 15:15:20

%S 12,14,12,45,12,14,12,17,12,14,12,33,12,14,12,20,12,14,12,25,12,14,12,

%T 17,12,14,12,20,12,14,12,30,12,14,12,25,12,14,12,17,12,14,12,30,12,14,

%U 12,22,12,14,12,69,12,14,12,17,12,14,12,22,12,14,12,22,12,14,12,82,12

%N Number of iteration that first becomes smaller than the initial value if Collatz-function (A006370) is iterated, starting with numbers of the form 64n + 59.

%C 1stSubmergeLengths[=A074473] with initial values belonging to other residue classes modulo 64 are either listed in A075476-A075483 or can be easily determined. For 64k+2s the first sink below initial value is at 2nd iterate; for 64k+4s+1 the first submerge below initial value comes at 4th term of iteration list; finally if initial value is of 64k+4s+3 form or moreover initial value = 64k+r, r = 3, 11, 19, 23, 35, 43, 51, 55, then for all k first sink emerges at the 7th, 9th, 7th, 9th, 7th, 9th, 7th, 9th iterates, respectively.

%H Antti Karttunen, <a href="/A075482/b075482.txt">Table of n, a(n) for n = 0..16384</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%F a(n) = A074473(64n + 59).

%e n=0: 64n + 59 = 59, the list = {59,178,89,268,134,67,202,101,304,152,76,38,...} the 12th term = 38 < 59 = the initial value, so a(0)=12.

%t Table[Function[m, Length@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, m, # >= m - 1 &]][64 n + 59], {n, 0, 84}] (* _Michael De Vlieger_, Mar 25 2017 *)

%o (PARI)

%o A006370(n) = if(n%2, 3*n+1, n/2);

%o A074473(n) = if(1==n,n,my(org_n=n); for(i=1,oo,if(n<org_n, return(i)); n = A006370(n)));

%o A075482(n) = A074473((64*n)+59); \\ _Antti Karttunen_, Oct 09 2018

%Y Cf. A006370, A074472, A074473, A075476, A075477-A075483.

%K nonn

%O 0,1

%A _Labos Elemer_, Sep 24 2002