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a(n) = (85*4^n - 1)/3.
0

%I #18 Nov 10 2023 18:31:30

%S 113,453,1813,7253,29013,116053,464213,1856853,7427413,29709653,

%T 118838613,475354453,1901417813,7605671253,30422685013,121690740053,

%U 486762960213,1947051840853,7788207363413,31152829453653,124611317814613,498445271258453,1993781085033813

%N a(n) = (85*4^n - 1)/3.

%C When any term in the sequence is iterated using the Collatz function, its trajectory's only odd number before reaching 1 will be 85.

%C Also, each term would have 2n+10 steps as its stopping time (A006577).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).

%e When n=5, a(5) = 29013 and when iterated using the Collatz function will have the following trajectory: 87040,43520,21760,10880,5440,2720,1360,680,340,170,85,256,128,64,32,16,8,4,2,1

%t (85*4^Range[25] - 1)/3 (* _Wesley Ivan Hurt_, Nov 10 2023 *)

%o (PARI) a(n) = 85*4^n\3 \\ _Charles R Greathouse IV_, Sep 09 2022

%Y Subsequence of A198584.

%Y Cf. A006577.

%K nonn,easy

%O 1,1

%A _Krishna Kumar Arumugam_, Sep 03 2022

%E Simpler definition and more terms from _Jon E. Schoenfield_, Sep 09 2022