A352894 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).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Apr 08 2022

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to 3x+1 (or Collatz) problem
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A000040, A005940, A064989, A139391, A156552, A286380, A329603, A341515, A352890, A352891, A352892, A352893.

Programs

PARI

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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)};
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 };
A329603(n) = A005940(2+(3*A156552(n)));
A341515(n) = if(n%2, A064989(n), A329603(n));
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
A352892(n) = A348717(A341515(n));
A352894(n) = if(n<=2, 0, my(k=0,x=n); while(x>=n, x = A352892(x); k++); (k));

Formula

a(2n+1) = 1 for n >= 1.

For n >= 1, a(n) <= A352891(n).

For n >= 1, a(n) <= A352893(n).