cp's OEIS Frontend

A352891 Number of iterations of map x -> A341515(x) needed to reach x < n when starting from x=n, or 0 if such number is never reached. Here A341515 is the Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).

%I A352891 #12 Apr 08 2022 22:40:37
%S A352891 0,0,1,6,1,3,1,11,1,3,1,9,1,7,1,11,1,3,1,6,1,6,1,9,1,11,1,7,1,1,1,91,
%T A352891 1,106,1,5,1,16,1,14,1,4,1,7,1,20,1,89,1,3,1,7,1,3,1,87,1,21,1,1,1,50,
%U A352891 1,92,1,5,1,18,1,3,1,8,1,98,1,14,1,5,1,14,1,34,1,6,1,35,1,12,1,2,1,21,1,71,1,90,1,3
%N A352891 Number of iterations of map x -> A341515(x) needed to reach x < n when starting from x=n, or 0 if such number is never reached. Here A341515 is the Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).
%C A352891 This is one possible analog for A102419 ("Dropping time" sequence) when computed for A341515. See also A352894.
%H A352891 Antti Karttunen, <a href="/A352891/b352891.txt">Table of n, a(n) for n = 1..10000</a>
%H A352891 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H A352891 <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F A352891 For n >= 1, a(2n+1) = 1.
%F A352891 For n >= 1, A352894(n) <= a(n) <= A352890(n).
%o A352891 (PARI)
%o A352891 A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o A352891 A064989(n) = {my(f); f = factor(n); if((n>1 && f[1,1]==2), f[1,2] = 0); for (i=1, #f~, f[i,1] = precprime(f[i,1]-1)); factorback(f)};
%o A352891 A156552(n) = { my(f = factor(n), p, p2 = 1, res = 0); for(i = 1, #f~, p = 1 << (primepi(f[i, 1]) - 1); res += (p * p2 * (2^(f[i, 2]) - 1)); p2 <<= f[i, 2]); res };
%o A352891 A329603(n) = A005940(2+(3*A156552(n)));
%o A352891 A341515(n) = if(n%2, A064989(n), A329603(n));
%o A352891 A352891(n) = if(n<=2, 0, my(k=0,x=n); while(x>=n, x = A341515(x); k++); (k));
%Y A352891 Cf. A000040, A005940, A006577, A064989, A156552, A329603, A352890, A352894.
%Y A352891 Cf. also A102419.
%K A352891 nonn
%O A352891 1,4
%A A352891 _Antti Karttunen_, Apr 08 2022