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, 7, 12, 136, 260, 4233, 8206, 87112285931760246646623899502532662136846, 174224571863520493293247799005065324265486, 1852673427797059126777135760139006525739432040582009271277945243629142736371850, 3705346855594118253554271520278013051304639509300498049262642688253220148478214

Offset: 2

Author

N. J. A. Sloane, Oct 24 2013

Keywords

• nonn

Comments

a(n) is the leading power of 2 in M(n) = A230303(n).

Examples

			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).
		

Links

• Max Alekseyev, Table giving values of n and an expression for a(n) for n=2..100
• Max A. Alekseyev and N. J. A. Sloane, On Kaprekar's Junction Numbers, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.
• Index entries for Colombian or self numbers and related sequences

Crossrefs

Cf. A228085, A230093, A230303 (for M(n)).

Programs

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)];

Extensions

a(11) corrected, expressions for a(2)-a(100) added by Max Alekseyev, Nov 02 2013