A348094 - OEIS

A348094

If the Collatz trajectory of n reaches 1, say after k steps, and there is an integer m > n such that T^i(m) and T^i(n) have the same parity for i = 0..k (where T^i denotes the i-th iterate of the Collatz map A006370), then a(n) is the least such m, otherwise a(n) is -1.

2, 4, 35, 8, 21, 70, 2055, 16, 8201, 42, 1035, 140, 141, 4110, 4111, 32, 529, 16402, 16403, 84, 85, 2070, 2071, 280, 65561, 282, 1180591620717411303451, 8220, 8221, 8222, 147573952589676412959, 64, 262177, 1058, 1059, 32804, 32805, 32806, 8388647, 168

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OFFSET

1,1

COMMENTS

When a(n) > 0, the binary expansion of A125711(n) is a prefix of that of A125711(a(n)).

LINKS

Paolo Xausa, Table of n, a(n) for n = 1..10000

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

FORMULA

a(2^k) = 2^(k+1) for any k >= 0.

a(n) = n + 2^A006666(n) when A006666(n) >= 0.

EXAMPLE