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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A084984 Numbers containing no prime digits. 28
0, 1, 4, 6, 8, 9, 10, 11, 14, 16, 18, 19, 40, 41, 44, 46, 48, 49, 60, 61, 64, 66, 68, 69, 80, 81, 84, 86, 88, 89, 90, 91, 94, 96, 98, 99, 100, 101, 104, 106, 108, 109, 110, 111, 114, 116, 118, 119, 140, 141, 144, 146, 148, 149, 160, 161, 164, 166, 168, 169 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

A193238(a(n)) = 0; complement of A118950. - Reinhard Zumkeller, Jul 19 2011

If n-1 is represented as a base-6 number (see A007092) according to n-1=d(m)d(m-1)...d(3)d(2)d(1)d(0) then a(n)= sum_{j=0..m} c(d(j))*10^j, where c(k)=0,1,4,6,8,9 for k=0..5. - Hieronymus Fischer, May 30 2012

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for 10-automatic sequences.

FORMULA

a(n) >> n^1.285. - Charles R Greathouse IV, Feb 20 2012

From Hieronymus Fischer, May 30 and Jun 25 2012: (Start)

a(n) = ((2*b_m(n)+1) mod 10 + floor((b_m(n)+4)/5) - floor((b_m(n)+1)/5))*10^m + sum_{j=0..m-1} ((2*b_j(n))) mod 12 + floor(b_j(n)/6) - floor((b_j(n)+1)/6) + floor((b_j(n)+4)/6) - floor((b_j(n)+5)/6)))*10^j, where n>1, b_j(n)) = floor((n-1-6^m)/6^j), m = floor(log_6(n-1)).

Special values:

a(1*6^n+1) = 1*10^n.

a(2*6^n+1) = 4*10^n.

a(3*6^n+1) = 6*10^n.

a(4*6^n+1) = 8*10^n.

a(5*6^n+1) = 9*10^n.

a(2*6^n) = 2*10^n - 1.

a(n) = 10^log_6(n-1) for n=6^k+1, k>0.

Inequalities:

a(n) < 10^log_6(n-1) for 6^k+1<n<=2*6^k, k>0.

a(n) > 10^log_6(n-1) for 2*6^k<n<=6*6^k, k>=0.

a(n) <= 4*10^(log_6(n-1)-log_6(2)) = 1.641372618*10^(log_6(n-1) , equality holds for n=2*6^k+1, k>=0.

a(n) > 2*10^(log_6(n-1)-log_6(2)) = 0.820686309*10^(log_6(n-1).

a(n) = A007092(n-1) iff the digits of A007092(n-1) are 0 or 1, a(n)>A007092(n-1), else.

a(n) >= A202267(n), equality holds if the representation of n-1 as a base-6 number has only digits 0 or 1.

Lower and upper limits:

lim inf a(n)/10^log_6(n) = 2/10^log_6(2) = 0.820686309, for n --> inf.

lim sup a(n)/10^log_6(n) = 4/10^log_6(2) = 1.641372618, for n --> inf.

where 10^log_6(n) = n^1.2850972089...

G.f.: g(x) = (x/(1-x))*sum_{j>=0} 10^j*x^6^j * (1-x^6^j)*((1+x^6^j)^4 + 4(1+2x^6^j) * x^(3*6^j))/(1-x^6^(j+1)).

Also: g(x) = (x/(1-x))*(h_(6,1)(x) + 3*h_(6,2)(x) + 2*h_(6,3)(x) + 2*h_(6,4)(x) + h_(6,5)(x) - 9*h_(6,6)(x)), where h_(6,k)(x) = sum_{j>=0} 10^j*x^(k*6^j)/(1-x^6^(j+1)).

(End)

EXAMPLE

166 has digits 1 and 6 and they are nonprime digits.

a(1000) = 8686.

a(10^4) = 118186

a(10^5) = 4090986.

a(10^6) = 66466686.

MATHEMATICA

npdQ[n_]:=And@@Table[FreeQ[IntegerDigits[n], i], {i, {2, 3, 5, 7}}]; Select[ Range[ 0, 200], npdQ] (* Harvey P. Dale, Jul 22 2013 *)

PROG

(Haskell)

a084984 n = a084984_list !! (n-1)

a084984_list = filter (not . any (`elem` "2357") . show ) [0..]

-- Reinhard Zumkeller, Jul 19 2011

(MAGMA) [n: n in [0..169] | forall{d: d in [2, 3, 5, 7] | d notin Set(Intseq(n))}];  // Bruno Berselli, Jul 19 2011

(PARI) is(n)=isprime(eval(Vec(Str(n))))==0 \\ Charles R Greathouse IV, Feb 20 2012

CROSSREFS

Cf. A046034, A034844 (primes).

Cf. A007092, A029581, A017042, A001743, A001744, A014263, A202267, A202268.

Sequence in context: A047748 A299540 A085558 * A104499 A137353 A167376

Adjacent sequences:  A084981 A084982 A084983 * A084985 A084986 A084987

KEYWORD

base,nonn

AUTHOR

Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 27 2003

EXTENSIONS

0 added by N. J. A. Sloane, Feb 02 2009

100 added by Arkadiusz Wesolowski, Mar 10 2011

Examples for n>=10^3 added by Hieronymus Fischer, May 30 2012

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 March 19 13:29 EDT 2019. Contains 321330 sequences. (Running on oeis4.)