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A347653
Partial sums of the trajectory of all positive integers in the 3x+1 or Collatz problem, including the trajectory [1, 4, 2, 1] of 1.
1
1, 5, 7, 8, 10, 11, 14, 24, 29, 45, 53, 57, 59, 60, 64, 66, 67, 72, 88, 96, 100, 102, 103, 109, 112, 122, 127, 143, 151, 155, 157, 158, 165, 187, 198, 232, 249, 301, 327, 340, 380, 400, 410, 415, 431, 439, 443, 445, 446, 454, 458, 460, 461, 470, 498, 512, 519, 541, 552, 586
OFFSET
1,2
EXAMPLE
The first two rows of A235795 are [1, 4, 2, 1]; [2, 1], so a(1)..a(6) are [1, 5, 7, 8, 10, 11].
MATHEMATICA
A235795row[n_]:=If[n==1, {1, 4, 2, 1}, NestWhileList[If[OddQ[#], 3#+1, #/2]&, n, #>1&]];
nrows=10; Accumulate[Flatten[Array[A235795row, nrows]]] (* Paolo Xausa, Jun 20 2022 *)
PROG
(PARI) f(n) = if (n%2, 3*n+1, n/2); \\ A014682
row(n) = {my(list=List()); listput(list, n); until(n==1, n = f(n); listput(list, n)); Vec(list); } \\ A235795
lista(nn) = {my(s=0, list = List()); for (n=1, nn, my(v = row(n)); for (k=1, #v, s += v[k]; listput(list, s); ); ); Vec(list); } \\ Michel Marcus, Sep 10 2021
CROSSREFS
Partial sums of A235795.
Cf. A006370, A235800, A347270 (all 3x+1 sequences).
Sequence in context: A189034 A112250 A192067 * A288735 A317507 A304433
KEYWORD
nonn,look
AUTHOR
Omar E. Pol, Sep 09 2021
STATUS
approved