login
Numbers of the form (2^(2*j + 6*k + 10) - 2^(2*j + 2) - 3)/9, with j,k >= 0.
1

%I #21 Aug 31 2021 16:47:54

%S 113,453,1813,7253,7281,29013,29125,116053,116501,464213,466005,

%T 466033,1856853,1864021,1864133,7427413,7456085,7456533,29709653,

%U 29824341,29826133,29826161,118838613,119297365,119304533,119304645,475354453,477189461,477218133

%N Numbers of the form (2^(2*j + 6*k + 10) - 2^(2*j + 2) - 3)/9, with j,k >= 0.

%C Sequence is a subsequence of A198584. When any term is iterated using the Collatz function, the last odd integer in the trajectory before 1 is of the form (4^(3*m + 4) - 1)/3.

%H Satya Das, <a href="https://www.researchgate.net/publication/354253993_3X1_PROBLEM_A_CONTINUOUS_EXTENSION_OF_THE_SPEEDED_UP_COLLATZ_MAP">Extension of speeded up Collatz map to the real line</a>

%t Take[Sort[Flatten[Table[(2^(2n1+6n2+10) - 2^(2n1+2) - 3)/9, {n1, 0, 20}, {n2, 0, 20}]]], 50]

%o (Python)

%o seq=[]

%o for n1 in range(20):

%o for n2 in range(20):

%o n=(2**(2*n1+6*n2+10) - 2**(2*n1+2) - 3)/9

%o seq.append(n)

%o seq.sort()

%o print(seq[0:50])

%Y Union with A342815 gives A198584.

%K nonn,easy

%O 1,1

%A _Satya Das_, Mar 22 2021