A230640 Let M(1)=0 and for n>1, B(n)=(M(ceiling(n/2))+M(floor(n/2))+2)/2, M(n)=3^B(n)+M(floor(n/2))+1. This sequence gives M(n).

0, 4, 28, 248, 129140168, 68630377364912, 2088595827392656793085408064780643444068898148936888424953199350296

Offset: 1

Author

N. J. A. Sloane, Oct 31 2013

Keywords

• nonn
• base

Links

• 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.

Crossrefs

Cf. A230639.

Related base-3 sequences: A053735, A134451, A230641, A230642, A230643, A230853, A230854, A230855, A230856, A230639, A230640, A010063 (trajectory of 1)

Smallest number m such that u + (sum of base-b digits of u) = m has exactly n solutions, for bases 2 through 10: A230303, A230640, A230638, A230867, A238840, A238841, A238842, A238843, A006064.

Programs

Maple

f:=proc(n) option remember; local B, M;
if n<=1 then RETURN([0, 0]);
else
B:=(f(ceil(n/2))[2] + f(floor(n/2))[2] + 2)/2;
M:=3^B+f(floor(n/2))[2]+1; RETURN([B, M]); fi;
end proc;
[seq(f(n)[2], n=1..7)];