[seqfan] Around Recaman, A231692 and A231693.

[Brigitte et Paul Curtz]

Dear all,

A005142 and differences:
0,  1,  3,   6,  2,  7,  13,  20, 12,  21, 11,..
1,  2,  3 , -4,  5,  6,  -7,   -8 ,  9,  -10,... .
Is the rank of the negative terms specified somewhere?

A231692/A231693 and differences:
0,       1,    1/2,  1/6,  5/12, 13/60,  1/20,  27/140, 19/280,  
451/2520,...
1,  -1/2,  -1/3,  1/4,   -1/5,    -1/6,     1/7,       -1/8,        1/9, 
          -1/10 ,... .
The rank of the negative terms must be written.

Inverse Akiyama-Tanigawa transform applied to  (-1)^n*A051716/A051717  
(in A190339):
1,         1/2,    1/12,   -5/18,  -431/720,...
1/2,     5/6,  13/12,  77/60,       29/20,  223/140,...    =g(n) 
=A064169/A231693(n+2)?   =(if unreduced: A027612/(n*A027611 with offset 1 ?)
-1/3,   -1/2,    -3/5,      -2/3,          -5/7,          -3/4,...
1/6,     1/5,      1/5,     4/21,        5/28,            1/6,...
-1/30,     0,     1/35,    1/21,        5/84,           1/15,... .

Note  1+2=3,  5+6=11,  13+12=25,  77+60=137,  29+30=49,. ...=A001008(n+1).

A231692(n+2)/A231693(n+2) +  g(n)=
2/2=1,   (1+5=6)/6=1,   (5+13=18)/12=3/2,   (13+77=90)/60=3/2,   
(1+29=30)/20=3/2,  (27+223=250)/140=25/14,... .

Best regards

Paul