login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(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)
OFFSET

1,2

COMMENTS

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).

REFERENCES

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

LINKS

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

Index entries for Colombian or self numbers and related sequences

FORMULA

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)).

EXAMPLE

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.

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

CROSSREFS

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

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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 October 17 15:01 EDT 2019. Contains 328116 sequences. (Running on oeis4.)