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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A245491 The least x > 0 such that x < the number of zero digits in the base-n expansions of the numbers 1 through x. 1
9, 87, 1068, 16022, 284704, 5834024, 135430302, 3511116537, 100559404366, 3152738985032, 107400330425888, 3950024143546665, 155996847068247395, 6584073072068125453, 295764262988176583800, 14088968131538370019982, 709394716006812244474473 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

If the function zeros(n,b) returns the number of zeros in the numbers 1 through n in base b, then:

zeros(2,2) = zeros_in(10) = 1.

zeros(4,2) = zeros_in(10,100) = 3.

zeros(5,2) = zeros_in(10,100,101) = 4.

zeros(6,2) = zeros_in(10,100,101,110) = 5.

zeros(8,2) = zeros_in(10,100,101,110,1000) = 8.

zeros(9,2) = zeros_in(10,100,101,110,1000,1001) = 10.

Therefore 9 < zeros(9,2) and 9 is the first entry in the list.

LINKS

Anthony Sand, Table of n, a(n) for n = 2..100

EXAMPLE

9 < zero(9,base=2) = 10.

87 < zero(87,3) = 88.

1068 < zero(1068,4) = 1069.

100559404366 < zero(100559404366,10) = 100559404367.

MATHEMATICA

a245491[n_Integer] := Module[{x = 0, z = 0},

While[x >= z, x++; z += Count[IntegerDigits[x, n], 0]]; x]; Map[a245491, Range[2, 12]] (* Michael De Vlieger, Aug 06 2014 *)

PROG

(PARI) /* formula for calculating n such that zero(n) > n, zero(n-1) <= (n-1) */

{estimate(x, b) = m1=b; est=x\b; nn=est; while(nn>0, d=nn%b; m2 = nn\b; if(d==0, est+=(x%m1)+1; if(m2>0, m2--)); est+=m1*m2; m1*=b; nn=nn\b); return(est)}

{bmin=2; bmx=20; for(bs=bmin, bmx, ni=bs^bs; n=bs+1; ez1=0; ez2=0; until(ez1>n && ez2<=n-1, ez = estimate(n, bs); if(n>=ez, n+=ni, n-=ni; if(ni>1, ni=ni\bs)); ez1 = estimate(n, bs); ez2 = estimate(n-1, bs)); print1(n, ", ")) } \\ Anthony Sand, Aug 11 2014

CROSSREFS

Cf. A164935.

Sequence in context: A267265 A152264 A035101 * A160466 A015583 A152266

Adjacent sequences:  A245488 A245489 A245490 * A245492 A245493 A245494

KEYWORD

nonn,base

AUTHOR

Anthony Sand, Jul 24 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 November 15 01:15 EST 2019. Contains 329142 sequences. (Running on oeis4.)