A348473 a(n) = Sum_{k=1..A003056(n)} 2^(T(n,k)-1), where T(n,k) = k-th term in row n of A235791.

1, 2, 5, 9, 18, 35, 69, 133, 266, 523, 1043, 2069, 4133, 8230, 16459, 32843, 65675, 131221, 262421, 524566, 1049127, 2097707, 4195371, 8389707, 16779341, 33556565, 67113110, 134221975, 268443799, 536879403, 1073758507, 2147500331, 4295000621, 8589967949, 17179935318

Offset

1,2

Comments

Decimal value of binary compactification of A235791.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..3322

Michael De Vlieger, bitmap of 10000 terms.

Michael De Vlieger, log-log scatterplot of a(n) for n-1..2^12.

Example

Row 3 of A235791 contains {3,1}, thus, a(3) = 2^(3-1) + 2(1-1)= 2^2 + 2^0 = 4+1 = 5.
Omar E. Pol's diagram of rows of A235791:
.                                    y         a(n)_2          a(n)
Row                                 _|    -------------------------
1                                 _|1| ->                1 =     1
2                               _|2 _| ->               10 =     2
3                             _|3  |1| ->              101 =     5
4                           _|4   _|1| ->             1001 =     9
5                         _|5    |2 _| ->            10010 =    18
6                       _|6     _|2|1| ->           100011 =    35
7                     _|7      |3  |1| ->          1000101 =    69
8                   _|8       _|3 _|1| ->         10000101 =   133
9                 _|9        |4  |2 _| ->        100001010 =   266
10              _|10        _|4  |2|1| ->       1000001011 =   523
11            _|11         |5   _|2|1| ->      10000010011 =  1043
12          _|12          _|5  |3  |1| ->     100000010101 =  2069
13        _|13           |6    |3 _|1| ->    1000000100101 =  4133
14      _|14            _|6   _|3|2 _| ->   10000000100110 =  8230
15    _|15             |7    |4  |2|1| ->  100000001001011 = 16459
16  _|16              _|7    |4  |2|1| -> 1000000001001011 = 32843
...

Mathematica

Table[Total@ Array[2^(-1 + Ceiling[(n + 1)/# - (# + 1)/2]) &, Floor[(Sqrt[8 n + 1] - 1)/2]], {n, 35}]
(* Regenerate k rows of A235791 using the b-file *)
With[{k = 120}, MapIndexed[1 + First[#2] - Position[IntegerDigits[#1, 2], 1][[All, 1]] &, Import["https://oeis.org/A348473/b348473.txt", "Data"][[1 ;; k, -1]]]] (* Michael De Vlieger, Oct 21 2021 *)

Crossrefs

Cf. A000079, A003056, A235791.

Sequence in context: A217210 A351983 A247322 * A097281 A321408 A289976

Adjacent sequences: A348470 A348471 A348472 * A348474 A348475 A348476

Keyword

nonn,easy

Author

Michael De Vlieger, Oct 19 2021

Status

approved