A341516 The Collatz or 3x+1 function T (A014682) conjugated by unary-binary-encoding (A156552).

1, 3, 2, 6, 3, 7, 5, 12, 4, 27, 7, 14, 11, 75, 6, 24, 13, 35, 17, 54, 10, 147, 19, 28, 9, 363, 8, 150, 23, 13, 29, 48, 14, 507, 15, 70, 31, 867, 22, 108, 37, 343, 41, 294, 12, 1083, 43, 56, 25, 63, 26, 726, 47, 175, 21, 300, 34, 1587, 53, 26, 59, 2523, 20, 96, 33, 847, 61, 1014, 38, 243, 67, 140, 71, 2883, 18, 1734

Offset

1,2

Comments

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

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to 3x+1 (or Collatz) problem

Index entries for sequences computed from indices in prime factorization

Formula

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

a(n) = A005940(1+A014682(A156552(n))).

Prog

(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), 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)));
A341516(n) = if(n%2, A064989(n), A064989(A329603(n)));

Crossrefs

Cf. A005940, A014682, A064989, A156552, A329603.

Cf. A341515 for a variant.

Sequence in context: A038572 A334667 A245676 * A060992 A064455 A141619

Adjacent sequences: A341513 A341514 A341515 * A341517 A341518 A341519

Keyword

nonn

Author

Antti Karttunen, Feb 15 2021

Status

approved