|
|
A230302
|
|
Let M(1)=0 and for n >= 2, let B(n)=M(ceiling(n/2))+M(floor(n/2))+2, M(n)=2^B(n)+M(floor(n/2))+1; sequence gives B(n).
|
|
2
|
|
|
2, 7, 12, 136, 260, 4233, 8206, 87112285931760246646623899502532662136846, 174224571863520493293247799005065324265486, 1852673427797059126777135760139006525739432040582009271277945243629142736371850, 3705346855594118253554271520278013051304639509300498049262642688253220148478214
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
2,1
|
|
COMMENTS
|
a(n) is the leading power of 2 in M(n) = A230303(n).
|
|
LINKS
|
Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory, 2022 (to appear).
|
|
EXAMPLE
|
The terms after 8206 are 2^136+4110, 2^137+14, 2^260+2^136+136, 2^261+262, 2^4233+2^260+260, ... (see also A230303).
|
|
MAPLE
|
f:=proc(n) option remember; local B, M;
if n<=1 then RETURN([0, 0]);
else
if (n mod 2) = 0 then B:=2*f(n/2)[2]+2;
else B:=f((n+1)/2)[2]+f((n-1)/2)[2]+2; fi;
M:=2^B+f(floor(n/2))[2]+1; RETURN([B, M]); fi;
end proc;
[seq(f(n)[1], n=1..7)];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
a(11) corrected, expressions for a(2)-a(100) added by Max Alekseyev, Nov 02 2013
|
|
STATUS
|
approved
|
|
|
|