cp's OEIS Frontend

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).

%I A230302 #53 Sep 05 2024 15:43:25
%S A230302 2,7,12,136,260,4233,8206,87112285931760246646623899502532662136846,
%T A230302 174224571863520493293247799005065324265486,
%U A230302 1852673427797059126777135760139006525739432040582009271277945243629142736371850,3705346855594118253554271520278013051304639509300498049262642688253220148478214
%N 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).
%C A230302 a(n) is the leading power of 2 in M(n) = A230303(n).
%H A230302 Max Alekseyev, <a href="/A230302/a230302_1.txt">Table giving values of n and an expression for a(n) for n=2..100</a>
%H A230302 Max A. Alekseyev and N. J. A. Sloane, <a href="https://arxiv.org/abs/2112.14365">On Kaprekar's Junction Numbers</a>, arXiv:2112.14365, 2021; Journal of Combinatorics and Number Theory 12:3 (2022), 115-155.
%H A230302 <a href="/index/Coi#Colombian">Index entries for Colombian or self numbers and related sequences</a>
%e A230302 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).
%p A230302 f:=proc(n) option remember; local B, M;
%p A230302 if n<=1 then RETURN([0,0]);
%p A230302 else
%p A230302 if (n mod 2) = 0 then B:=2*f(n/2)[2]+2;
%p A230302    else B:=f((n+1)/2)[2]+f((n-1)/2)[2]+2; fi;
%p A230302 M:=2^B+f(floor(n/2))[2]+1; RETURN([B,M]); fi;
%p A230302 end proc;
%p A230302 [seq(f(n)[1],n=1..7)];
%Y A230302 Cf. A228085, A230093, A230303 (for M(n)).
%K A230302 nonn
%O A230302 2,1
%A A230302 _N. J. A. Sloane_, Oct 24 2013
%E A230302 a(11) corrected, expressions for a(2)-a(100) added by _Max Alekseyev_, Nov 02 2013