cp's OEIS Frontend

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.

%I A348473 #8 Oct 22 2021 11:36:10
%S A348473 1,2,5,9,18,35,69,133,266,523,1043,2069,4133,8230,16459,32843,65675,
%T A348473 131221,262421,524566,1049127,2097707,4195371,8389707,16779341,
%U A348473 33556565,67113110,134221975,268443799,536879403,1073758507,2147500331,4295000621,8589967949,17179935318
%N 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.
%C A348473 Decimal value of binary compactification of A235791.
%H A348473 Michael De Vlieger, <a href="/A348473/b348473.txt">Table of n, a(n) for n = 1..3322</a>
%H A348473 Michael De Vlieger, <a href="/A348473/a348473.png">bitmap of 10000 terms</a>.
%H A348473 Michael De Vlieger, <a href="/A348473/a348473_1.png">log-log scatterplot of a(n)</a> for n-1..2^12.
%e A348473 Row 3 of A235791 contains {3,1}, thus, a(3) = 2^(3-1) + 2(1-1)= 2^2 + 2^0 = 4+1 = 5.
%e A348473 Omar E. Pol's diagram of rows of A235791:
%e A348473 .                                    y         a(n)_2          a(n)
%e A348473 Row                                 _|    -------------------------
%e A348473 1                                 _|1| ->                1 =     1
%e A348473 2                               _|2 _| ->               10 =     2
%e A348473 3                             _|3  |1| ->              101 =     5
%e A348473 4                           _|4   _|1| ->             1001 =     9
%e A348473 5                         _|5    |2 _| ->            10010 =    18
%e A348473 6                       _|6     _|2|1| ->           100011 =    35
%e A348473 7                     _|7      |3  |1| ->          1000101 =    69
%e A348473 8                   _|8       _|3 _|1| ->         10000101 =   133
%e A348473 9                 _|9        |4  |2 _| ->        100001010 =   266
%e A348473 10              _|10        _|4  |2|1| ->       1000001011 =   523
%e A348473 11            _|11         |5   _|2|1| ->      10000010011 =  1043
%e A348473 12          _|12          _|5  |3  |1| ->     100000010101 =  2069
%e A348473 13        _|13           |6    |3 _|1| ->    1000000100101 =  4133
%e A348473 14      _|14            _|6   _|3|2 _| ->   10000000100110 =  8230
%e A348473 15    _|15             |7    |4  |2|1| ->  100000001001011 = 16459
%e A348473 16  _|16              _|7    |4  |2|1| -> 1000000001001011 = 32843
%e A348473 ...
%t A348473 Table[Total@ Array[2^(-1 + Ceiling[(n + 1)/# - (# + 1)/2]) &, Floor[(Sqrt[8 n + 1] - 1)/2]], {n, 35}]
%t A348473 (* Regenerate k rows of A235791 using the b-file *)
%t A348473 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 *)
%Y A348473 Cf. A000079, A003056, A235791.
%K A348473 nonn,easy
%O A348473 1,2
%A A348473 _Michael De Vlieger_, Oct 19 2021