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A355090 Square array A(n, k), n >= 0, k > 0, read by antidiagonals upwards; A(n, k) is the unique m such that n/k = fusc(m)/fusc(m+1) (where fusc is Stern's diatomic series A002487).

%I A355090 #13 Jun 20 2022 04:27:16
%S A355090 0,1,0,3,2,0,7,1,4,0,15,5,6,8,0,31,3,1,2,16,0,63,11,9,14,12,32,0,127,
%T A355090 7,13,1,10,4,64,0,255,23,3,17,30,2,24,128,0,511,15,19,5,1,6,28,8,256,
%U A355090 0,1023,47,27,29,33,62,18,20,48,512,0,2047,31,7,3,25,1,22,2,4,16,1024,0
%N A355090 Square array A(n, k), n >= 0, k > 0, read by antidiagonals upwards; A(n, k) is the unique m such that n/k = fusc(m)/fusc(m+1) (where fusc is Stern's diatomic series A002487).
%C A355090 The binary expansion of A(n, k) encodes the position of n/k (> 0) in the Calkin-Wilf tree.
%H A355090 Rémy Sigrist, <a href="/A355090/b355090.txt">Table of n, a(n) for n = 0..10152</a>
%H A355090 Wikipedia, <a href="https://en.wikipedia.org/wiki/Calkin%E2%80%93Wilf_tree">Calkin-Wilf tree</a>
%H A355090 <a href="/index/St#Stern">Index entries for sequences related to Stern's sequences</a>
%F A355090 A(m*n, m*k) = A(n, k) for any m > 0.
%F A355090 A(k, n) = A054429(A(n, k)) for any n, k > 0.
%F A355090 A(0, k) = 0.
%F A355090 A(1, k) = 2^(k-1).
%F A355090 A(n, 1) = 2^n - 1.
%F A355090 A(n, n+1) = A000918(n+1).
%F A355090 A(A002487(n), A002487(n+1)) = n.
%e A355090 Square array A(n, k) begins:
%e A355090   n\k|      1    2    3    4    5    6    7    8    9    10    11    12
%e A355090   ---+-----------------------------------------------------------------
%e A355090     0|      0    0    0    0    0    0    0    0    0     0     0     0
%e A355090     1|      1    2    4    8   16   32   64  128  256   512  1024  2048
%e A355090     2|      3    1    6    2   12    4   24    8   48    16    96    32
%e A355090     3|      7    5    1   14   10    2   28   20    4    56    40     8
%e A355090     4|     15    3    9    1   30    6   18    2   60    12    36     4
%e A355090     5|     31   11   13   17    1   62   22   26   34     2   124    44
%e A355090     6|     63    7    3    5   33    1  126   14    6    10    66     2
%e A355090     7|    127   23   19   29   25   65    1  254   46    38    58    50
%e A355090     8|    255   15   27    3   21    9  129    1  510    30    54     6
%e A355090     9|    511   47    7   35   61    5   49  257    1  1022    94    14
%e A355090    10|   1023   31   39   11    3   13   57   17  513     1  2046    62
%e A355090    11|   2047   95   55   59   67  125   37   41   97  1025     1  4094
%e A355090    12|   4095   63   15    7   51    3   45    5    9    33  2049     1
%o A355090 (PARI) A(x,y) = { if (x==0, 0, my (v=0,t=1,a=0,b=1,c=1,d=0); while (1, my (m=a+c, n=b+d); if (x*n==y*m, return (t+v), x*n<y*m, [c,d]=[m,n], [v,a,b]=[v+t,m,n]); t*=2)) }
%Y A355090 Cf. A000918, A002487, A054429.
%K A355090 nonn,tabl
%O A355090 0,4
%A A355090 _Rémy Sigrist_, Jun 18 2022