The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.



Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A230303 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 M(n). 12
0, 5, 129, 4102, 87112285931760246646623899502532662132742, 1852673427797059126777135760139006525652319754650249024631321344126610074239106 (list; graph; refs; listen; history; text; internal format)



M(n) is the smallest value of k such that A228085(k) = n. For example, 129 is the first time a 3 appears in A228085 (and is therefore the first term in A230092). M(4) = 4102 is the first time a 4 appears in A228085 (and is therefore the first term in A227915).


Max A. Alekseyev, Donovan Johnson and N. J. A. Sloane, On Kaprekar's Junction Numbers, in preparation, 2017.


Table of n, a(n) for n=1..6.

Index entries for Colombian or self numbers and related sequences


Define i by 2^(i-1) < n <= 2^i. Then it appears that

a(n) = 2^2^2^...^2^x

a tower of height i+3, containing i+2 2's, where x is in the range 0 < x <= 1.

For example, if n=7, i=3, and

a(18) = 2^4233+130 = 2^2^2^2^2^.88303276...

Note also that i+2 = A230864(a(n)).


The terms are 0, 2^2+0+1, 2^7+0+1, 2^12+5+1, 2^136+5+1, 2^160+129+1, 2^4233+129+1, 2^8206+4102+1, 2^k+4102+1 with k=2^136+4110, ... .

The length (in bits) of the n-th term is A230302(n)+1.


f:=proc(n) option remember; local B, M;

if n<=1 then RETURN([0, 0]);


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)[2], n=1..6)];


Cf. A228085, A230092, A227915, A230093, A230302 (for B(n)), A230864.

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.

Sequence in context: A316986 A316392 A277259 * A094074 A012218 A012136

Adjacent sequences:  A230300 A230301 A230302 * A230304 A230305 A230306




N. J. A. Sloane, Oct 24 2013; Mar 26 2014



Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 20 14:02 EST 2020. Contains 331094 sequences. (Running on oeis4.)