%I #9 Apr 09 2022 08:47:24
%S 0,0,1,2,1,1,1,4,1,1,1,3,1,2,1,4,1,1,1,2,1,2,1,3,1,3,1,2,1,1,1,35,1,
%T 40,1,2,1,5,1,5,1,1,1,2,1,6,1,34,1,1,1,2,1,1,1,33,1,6,1,1,1,17,1,35,1,
%U 1,1,6,1,1,1,3,1,35,1,4,1,1,1,5,1,10,1,3,1,10,1,4,1,1,1,6,1,24,1,34,1,1,1,2,1
%N Number of iterations of map x -> A352892(x) needed to reach x < n when starting from x=n, or 0 if such number is never reached. Here A352892 is the next odd term in the Collatz or 3x+1 map (A139391) conjugated by unary-binary-encoding (A156552).
%H Antti Karttunen, <a href="/A352894/b352894.txt">Table of n, a(n) for n = 1..16384</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>
%F a(2n+1) = 1 for n >= 1.
%F For n >= 1, a(n) <= A352891(n).
%F For n >= 1, a(n) <= A352893(n).
%o (PARI)
%o A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
%o 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 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 A329603(n) = A005940(2+(3*A156552(n)));
%o A341515(n) = if(n%2, A064989(n), A329603(n));
%o A348717(n) = { my(f=factor(n)); if(#f~>0, my(pi1=primepi(f[1, 1])); for(k=1, #f~, f[k, 1] = prime(primepi(f[k, 1])-pi1+1))); factorback(f); }; \\ From A348717
%o A352892(n) = A348717(A341515(n));
%o A352894(n) = if(n<=2, 0, my(k=0,x=n); while(x>=n, x = A352892(x); k++); (k));
%Y Cf. A000040, A005940, A064989, A139391, A156552, A286380, A329603, A341515, A352890, A352891, A352892, A352893.
%K nonn
%O 1,4
%A _Antti Karttunen_, Apr 08 2022