A352892 -id:A352892 - cp's OEIS frontend

A352893 Number of iterations of map x -> A352892(x) needed to reach x <= 2 when starting from x=n, or -1 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, 5, 3, 6, 1, 4, 1, 3, 2, 5, 1, 2, 1, 6, 7, 8, 1, 4, 3, 8, 6, 3, 1, 1, 1, 39, 4, 44, 2, 41, 1, 44, 9, 11, 1, 6, 1, 8, 5, 10, 1, 38, 3, 7, 9, 8, 1, 5, 7, 37, 45, 10, 1, 9, 1, 56, 7, 39, 4, 3, 1, 44, 45, 40, 1, 41, 1, 39, 3, 44, 2, 8, 1, 11, 6, 15, 1, 3, 9, 15, 11, 13, 1, 4, 7, 10, 11, 32, 9, 38

Offset: 1

Antti Karttunen, Apr 08 2022

nonn

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to 3x+1 (or Collatz) problem
Index entries for sequences computed from indices in prime factorization

Cf. A000040, A005940, A064989, A139391, A156552, A286380, A329603, A341515, A352890, A352892, A352894.

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));
A352893(n) = { my(k=0); while(n>2, n = A352892(n); k++); (k); };

\\ Much faster than above program:
A139391(n) = my(x = if(n%2, 3*n+1, n/2)); x/2^valuation(x, 2); \\ From A139391
A286380(n) = { my(k=0); while(n>1, n = A139391(n); k++); (k); };
A352893(n) = if(1==n,0,A286380(A156552(n)));

If n <= 2, a(n) = 0, otherwise a(n) = 1 + a(A352892(n)).
For n > 1, a(n) = A286380(A156552(n)).
a(p) = 1 for all odd primes p.
For n >= 1, A352894(n) <= a(n) <= A352890(n).

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).

Original entry on oeis.org

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

Antti Karttunen, Apr 08 2022

nonn

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

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));

a(2n+1) = 1 for n >= 1.
For n >= 1, a(n) <= A352891(n).
For n >= 1, a(n) <= A352893(n).

A352896 Maximum value of bigomega (A001222) computed for the terms x after the initial n, when map x -> A352892(x) is iterated starting from x=n down to the first x <= 2, or -1 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).

Original entry on oeis.org

0, 1, 1, 2, 1, 1, 1, 3, 2, 3, 1, 3, 1, 3, 2, 4, 1, 2, 1, 4, 3, 4, 1, 4, 2, 3, 3, 4, 1, 1, 1, 8, 3, 8, 2, 8, 1, 8, 4, 5, 1, 3, 1, 4, 3, 6, 1, 8, 2, 4, 3, 4, 1, 3, 3, 8, 8, 5, 1, 3, 1, 8, 4, 8, 3, 3, 1, 8, 8, 8, 1, 8, 1, 8, 3, 8, 2, 4, 1, 6, 4, 7, 1, 4, 4, 7, 6, 5, 1, 3, 3, 6, 5, 8, 3, 8, 1, 3, 4, 4, 1, 3, 1, 8, 3

Offset: 1

Antti Karttunen, Apr 08 2022

Equally, maximum value of bigomega (A001222) computed for the terms x after the initial n, when map x -> A341515(x) is iterated starting from x=n.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to 3x+1 (or Collatz) problem
Index entries for sequences computed from indices in prime factorization

Cf. A000040, A001222, A005940, A064989, A156552, A329603, A341515, A352892, A352895, A352897, A352899.

A352896(n) = if(n<=2,n-1, my(m=0); while(n>2, n = A352892(n); m = max(m,bigomega(n))); (m)); \\ Needs also code from A352892.

A352896(n) = if(n<=2,n-1,my(m=0); while(n>2, n = A341515(n); m = max(m,bigomega(n))); (m)); \\ Slower, but equivalent.

\\ Faster:
A139391(n) = my(x = if(n%2, 3*n+1, n/2)); x/2^valuation(x, 2); \\ From A139391
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 };
A352895(n) = { my(mw=1); while(n>1, n = A139391(n); mw = max(hammingweight(n),mw)); (mw); };
A352896(n) = if(1==n,0,A352895(A156552(n)));

a(n) = A352897(A341515(n)) = A352897(A352892(n)).

For n > 1, a(n) = A352895(A156552(n)).

A352897 Maximum value of bigomega (A001222) computed for all the terms x (including the starting term x=n), when map x -> A352892(x) is iterated down to the first x <= 2, or -1 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).

Original entry on oeis.org

0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 1, 3, 1, 3, 2, 4, 1, 3, 1, 4, 3, 4, 1, 4, 2, 3, 3, 4, 1, 3, 1, 8, 3, 8, 2, 8, 1, 8, 4, 5, 1, 3, 1, 4, 3, 6, 1, 8, 2, 4, 3, 4, 1, 4, 3, 8, 8, 5, 1, 4, 1, 8, 4, 8, 3, 3, 1, 8, 8, 8, 1, 8, 1, 8, 3, 8, 2, 4, 1, 6, 4, 7, 1, 4, 4, 7, 6, 5, 1, 4, 3, 6, 5, 8, 3, 8, 1, 3, 4, 4, 1, 3, 1, 8, 3

Offset: 1

Antti Karttunen, Apr 08 2022

nonn

Equally, maximum value of bigomega (A001222) computed for all the terms x (including the starting term x=n), when map x -> A341515(x) is iterated starting from x=n.

Antti Karttunen, Table of n, a(n) for n = 1..16384
Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
Index entries for sequences related to 3x+1 (or Collatz) problem
Index entries for sequences computed from indices in prime factorization

Cf. A001222, A156552, A333860, A341515, A352892, A352896, A352898.

A352897(n) = { my(m=bigomega(n)); while(n>2, m = max(m,bigomega(n)); n = A352892(n)); (m); }; \\ Uses the code from A352892.

A352897(n) = { my(m=bigomega(n)); while(n>2, m = max(m,bigomega(n)); n = A341515(n)); (m); }; \\ Slightly slower.

A139391(n) = my(x = if(n%2, 3*n+1, n/2)); x/2^valuation(x, 2); \\ From A139391
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 };
A333860(n) = { my(mw=1); while(n>1, mw = max(hammingweight(n),mw); n = A139391(n)); (mw); };
A352897(n) = if(1==n,0,A333860(A156552(n)));

a(n) = max(A001222(n), A352896(n)).

For n > 1, a(n) = A333860(A156552(n)).

A352898 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A046523(n), A352892(n)], except f(n) = -n when <= 2.

Original entry on oeis.org

1, 2, 3, 4, 3, 5, 3, 6, 7, 8, 3, 9, 3, 10, 11, 12, 3, 13, 3, 14, 15, 16, 3, 17, 7, 18, 19, 20, 3, 21, 3, 22, 23, 24, 11, 25, 3, 26, 27, 28, 3, 29, 3, 30, 31, 32, 3, 33, 7, 34, 35, 36, 3, 37, 15, 38, 39, 40, 3, 41, 3, 42, 34, 43, 23, 44, 3, 45, 46, 47, 3, 48, 3, 49, 50, 51, 11, 52, 3, 53, 54, 55, 3, 56, 27, 57, 58, 59, 3, 60, 15

Offset: 1

Antti Karttunen, Apr 08 2022

nonn

For all i, j: A305801(i) = A305801(j) => a(i) = a(j) => A352897(i) = A352897(j).

Cf. A046523, A101296, A305801, A305897, A352892, A352897, A352899.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); };  \\ From A046523
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));
Aux352898(n) = if(n<=2,-n,[A046523(n),A352892(n)]);
v352898 = rgs_transform(vector(up_to, n, Aux352898(n)));
A352898(n) = v352898[n];

A352899 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A352892(n), except f(n) = -n when <= 2.

Original entry on oeis.org

1, 2, 3, 4, 3, 3, 3, 5, 6, 7, 3, 8, 3, 9, 4, 10, 3, 4, 3, 11, 12, 13, 3, 14, 6, 15, 7, 16, 3, 3, 3, 17, 8, 18, 4, 19, 3, 20, 21, 22, 3, 7, 3, 23, 5, 24, 3, 25, 6, 26, 27, 28, 3, 5, 12, 29, 30, 31, 3, 27, 3, 32, 26, 33, 8, 9, 3, 34, 35, 36, 3, 37, 3, 38, 9, 39, 4, 13, 3, 40, 41, 42, 3, 43, 21, 44, 45, 46, 3, 8, 12

Offset: 1

Antti Karttunen, Apr 08 2022

nonn

Restricted growth sequence transform of function f(n) = -n if n < 3, and otherwise f(n) = A352892(n).
For all i, j:
  A305801(i) = A305801(j) => A352898(i) = A352898(j) => a(i) = a(j),
  a(i) = a(j) => A352893(i) = A352893(j),
  a(i) = a(j) => A352896(i) = A352896(j).

Cf. A305801, A329603, A341515, A348717, A352892, A352893, A352896, A352898.

up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
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));
Aux352899(n) = if(n<=2,-n,A352892(n));
v352899 = rgs_transform(vector(up_to, n, Aux352899(n)));
A352899(n) = v352899[n];

A341515 The Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).

Original entry on oeis.org

1, 5, 2, 15, 3, 11, 5, 45, 4, 125, 7, 33, 11, 245, 6, 135, 13, 77, 17, 375, 10, 605, 19, 99, 9, 845, 8, 735, 23, 17, 29, 405, 14, 1445, 15, 231, 31, 1805, 22, 1125, 37, 1331, 41, 1815, 12, 2645, 43, 297, 25, 275, 26, 2535, 47, 539, 21, 2205, 34, 4205, 53, 51, 59, 4805, 20, 1215, 33, 1859, 61, 4335, 38, 3125, 67, 693

Offset: 1

Antti Karttunen, Feb 14 2021

nonn

Collatz-conjecture can be formulated via this sequence by postulating that all iterations of a(n), starting from any n > 1, will eventually reach the cycle [2, 5, 3].

Cf. A005940, A006370, A064989, A156552, A329603, A341510, A347115 (Möbius transform),
Sequences related to iterations of this sequence: A352890, A352891, A352892, A352893, A352894, A352896, A352897, A352898, A352899.
Cf. A341516 (a variant).

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), 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));

If n is odd, then a(n) = A064989(n), otherwise a(n) = A329603(n) = A341510(n,2*n).

a(n) = A005940(1+A006370(A156552(n))).

A352890 Number of iterations of map x -> A341515(x) needed to reach x <= 2 when starting from x=n, or -1 if such number is never reached. Here A341515 is the Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).

Original entry on oeis.org

0, 0, 1, 7, 2, 5, 3, 16, 8, 19, 4, 14, 5, 12, 6, 17, 6, 9, 7, 20, 20, 26, 8, 15, 9, 27, 17, 13, 9, 7, 10, 106, 13, 121, 7, 111, 11, 122, 27, 34, 12, 21, 13, 27, 15, 35, 14, 104, 10, 23, 28, 28, 15, 18, 21, 102, 122, 36, 16, 29, 17, 156, 21, 107, 14, 14, 18, 122, 123, 109, 19, 112, 20, 113, 10, 123, 8, 28, 21, 35

Offset: 1

Antti Karttunen, Apr 08 2022

The unbroken ray in the scatter plot corresponds to primes.

Cf. A000040, A005940, A006577, A064989, A156552, A329603, A341515.

Cf. also A352891, A352892, A352893, A352894.

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));
A352890(n) = { my(k=0); while(n>2, n = A341515(n); k++); (k); };

If n <= 2, a(n) = 0, otherwise a(n) = 1 + a(A341515(n)).
For n > 1, a(n) = A006577(A156552(n)).
For n >= 1, a(A000040(n)) = n-1.
For n >= 1, a(n) >= A352891(n).
For n >= 1, a(n) >= A352893(n).

A353267 The least number with the same prime factorization pattern (A348717) as A332449(n) = A005940(1+(3*A156552(n))).

Original entry on oeis.org

1, 4, 4, 10, 4, 16, 4, 30, 10, 36, 4, 22, 4, 100, 16, 90, 4, 40, 4, 250, 36, 196, 4, 66, 10, 484, 30, 490, 4, 64, 4, 270, 100, 676, 16, 154, 4, 1156, 196, 750, 4, 144, 4, 1210, 22, 1444, 4, 198, 10, 84, 484, 1690, 4, 120, 36, 1470, 676, 2116, 4, 34, 4, 3364, 250, 810, 100, 400, 4, 2890, 1156, 324, 4, 462, 4, 3844

Offset: 1

Antti Karttunen, Apr 09 2022

nonn

Index entries for sequences computed from indices in prime factorization

Cf. A005940, A156552, A332449, A348717.

Cf. also A305897 (rgs-transform), A352892, A353268.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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 };
A332449(n) = A005940(1+(3*A156552(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
A353267(n) = A348717(A332449(n));

a(n) = A348717(A332449(n)) = A332449(A348717(n)).

A353268 The least number with the same prime factorization pattern (A348717) as A329603(n) = A005940(1+(1+(3*A156552(n)))).

Original entry on oeis.org

2, 2, 8, 6, 18, 2, 50, 12, 20, 8, 98, 14, 242, 18, 32, 24, 338, 6, 578, 54, 72, 50, 722, 28, 42, 98, 60, 150, 1058, 2, 1682, 48, 200, 242, 162, 70, 1922, 338, 392, 108, 2738, 8, 3362, 294, 44, 578, 3698, 56, 110, 20, 968, 726, 4418, 12, 450, 300, 1352, 722, 5618, 26, 6962, 1058, 500, 96, 882, 18, 7442, 1014, 2312

Offset: 1

Antti Karttunen, Apr 09 2022

nonn

Index entries for sequences computed from indices in prime factorization

Cf. A005940, A156552, A348717, A353267.

Coincides with A352892 on even n, and with A329603 on odd n.

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); (t); };
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)));
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
A353268(n) = A348717(A329603(n));

a(n) = A348717(A329603(n)).

For all n >= 1, a(2n) = A352892(2n), a(2n-1) = A329603(2n-1).

cp's OEIS Frontend

A352893 Number of iterations of map x -> A352892(x) needed to reach x <= 2 when starting from x=n, or -1 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).

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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).

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A352898 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = [A046523(n), A352892(n)], except f(n) = -n when <= 2.

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A352899 Lexicographically earliest infinite sequence such that a(i) = a(j) => f(i) = f(j), where f(n) = A352892(n), except f(n) = -n when <= 2.

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A341515 The Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).

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A352890 Number of iterations of map x -> A341515(x) needed to reach x <= 2 when starting from x=n, or -1 if such number is never reached. Here A341515 is the Collatz or 3x+1 map (A006370) conjugated by unary-binary-encoding (A156552).

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