A347269 - OEIS

%I #39 Sep 07 2021 04:11:23

%S 4,5,6,11,14,15,18,19,25,32,33,40,42,43,47,48,52,53,57,59,62,63,68,69,

%T 70,75,78,79,82,83,88,90,91,92,93,105,108,109,110,112,116,117,120,121,

%U 122,135,139,144,145,146,147,148,149,152,154,161,162,163,175,185,187,191,193

%N a(n) is the first term of the n-th 3x+1 sequence that shares infinitely many 1's with the 3x+1 sequence that starts at 4.

%C a(n) is the first term of the row a(n) of the square array A347270.

%C Integers m such that A008908(m) == 0 (mod 3). - _Michel Marcus_, Aug 31 2021

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%e From _Michel Marcus_ and _Omar E. Pol_, Aug 31 2021: (Start)

%e Excerpt from A347270 array showing that the 3x+1 sequences that start at 4, 5, 6, 11 and 14 share infinitely many 1's.

%e    4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...

%e    5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...

%e    6, 3,10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...

%e   11,34,17,52,26,13,40,20,10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...

%e   14, 7,22,11,34,17,52,26,13,40,20,10, 5,16, 8, 4, 2, 1, 4, 2, 1, ... (End)

%o (PARI) f(n) = if (n%2, 3*n+1, n/2); \\ A006370

%o nb(n) = my(k=1, m=n); while (m!=1, k++; m=f(m)); k; \\ A008908

%o isok(m) = (nb(m) % 3) == 0; \\ _Michel Marcus_, Aug 31 2021

%Y Companion of A347267 and A347268.

%Y Cf. A006370, A033478, A033479, A075884, A076536, A153727, A347270.

%K nonn

%O 1,1

%A _Omar E. Pol_, Aug 25 2021

%E More terms from _Michel Marcus_, Aug 31 2021