A372443 The n-th iterate of 27 with Reduced Collatz-function R, which gives the odd part of 3n+1.

27, 41, 31, 47, 71, 107, 161, 121, 91, 137, 103, 155, 233, 175, 263, 395, 593, 445, 167, 251, 377, 283, 425, 319, 479, 719, 1079, 1619, 2429, 911, 1367, 2051, 3077, 577, 433, 325, 61, 23, 35, 53, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Author

Antti Karttunen, May 01 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A000265, A075677, A371093.

Column 14 of A372283, Row 13 of A256598 (but only up to the first 1).

Row 1 of A372560.

From term 47 to the first 1 same as A088593.

Sequences derived from this one or related to:

A372444,

A372445 column index of a(n) in array A257852,

A372362 the 2-adic valuation of 1 + 3*a(n), equal to row index of a(n) in array A257852,

A372447 binary lengths minus 1,

A372446 a(n) xored with the term of A086893 having the same binary length,

A372453 a(n) minus the term of A086893 having the same binary length.

Programs

PARI

R(n) = { n = 1+3*n; n>>valuation(n, 2); };
A372443(n) = { my(x=27); while(n, x=R(x); n--); (x); };

Formula

a(0) = 27; for n > 0, a(n) = R(a(n-1)), where R(n) = (3*n+1)/2^A371093(n) = A000265(3*n+1).

For n > 0, a(n) = R(A372444(n-1)) = A000265(1+3*A372444(n-1)).