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%I #38 Sep 04 2021 01:48:11
%S 1,8,10,12,13,17,22,23,27,28,29,30,36,37,38,49,50,51,64,65,66,67,71,
%T 80,84,85,86,87,89,94,95,96,103,104,106,111,113,114,115,118,119,124,
%U 125,126,136,137,138,140,141,150,151,153,156,157,158,159,164,165,166,176,180
%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 1.
%C a(n) is the first term of the row a(n) of the square array A347270.
%C Integers m such that A008908(m) == 1 (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 1, 8, 10, 12 and 13 share infinitely many 1's.
%e 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
%e 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
%e 10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
%e 12, 6, 3,10, 5,16, 8, 4, 2, 1, 4, 2, 1, 4, 2, 1, 4, 2, 1, ...
%e 13,40,20,10, 5,16, 8, 4, 2, 1, 4, 2, 1, 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) == 1; \\ _Michel Marcus_, Aug 31 2021
%Y Companion of A347268 and A347269.
%Y Cf. A006370, A008908, A033478, A033479, A075884, A076536, A153727, A347270.
%K nonn
%O 1,2
%A _Omar E. Pol_, Aug 25 2021
%E More terms from _Michel Marcus_, Aug 31 2021
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