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
Examples
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
...
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.
Programs
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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 *)
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