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A202268 Numbers in which all digits are nonprimes (1, 4, 6, 8, 9). 16
1, 4, 6, 8, 9, 11, 14, 16, 18, 19, 41, 44, 46, 48, 49, 61, 64, 66, 68, 69, 81, 84, 86, 88, 89, 91, 94, 96, 98, 99, 111, 114, 116, 118, 119, 141, 144, 146, 148, 149, 161, 164, 166, 168, 169, 181, 184, 186, 188, 189, 191, 194, 196, 198, 199, 411, 414, 416, 418, 419 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Supersequence of A029581.

Subsequence of A084984.

If n-1 is represented as a zerofree base-5 number (see A084545) 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)=1,4,6,8,9 for k=1..5. - Hieronymus Fischer, May 30 2012

LINKS

Hieronymus Fischer, Table of n, a(n) for n = 1..10000

Index entries for 10-automatic sequences.

FORMULA

From Hieronymus Fischer, May 30 2012: (Start)

a(n) = Sum_{j=0..m-1} ((2*b_j(n)+1) mod 10 + floor((b_j(n)+4)/5) - floor((b_j(n)+1)/5))*10^j, where b_j(n))=floor((4*n+1-5^m)/(4*5^j)), m=floor(log_5(4*n+1)).

a(1*(5^n-1)/4) = 1*(10^n-1)/9.

a(2*(5^n-1)/4) = 4*(10^n-1)/9.

a(3*(5^n-1)/4) = 6*(10^n-1)/9.

a(4*(5^n-1)/4) = 8*(10^n-1)/9.

a(5*(5^n-1)/4) = 10^n-1.

a(n) = (10^log_5(4*n+1)-1)/9 for n=(5^k-1)/4, k>0.

a(n) <= 36/(9*2^log_5(9)-1)*(10^log_5(4*n+1)-1)/9 for n>0, equality holds for n=2.

a(n) > 0.776*10^log_5(4*n+1)-1)/9 for n>0.

a(n) >= A001742(n), equality holds for n=(5^k-1)/4, k>0.

a(n) = A084545(n) iff all digits of A084545(n) are 1, a(n)>A084545(n), else.

G.f.: g(x) = (x^(1/4)*(1-x))^(-1) Sum_{j>=0} 10^j*z(j)^(5/4)*(1-z(j))*(1 + 4z(j) + 6*z(j)^2 + 8*z(j)^3 + 9*z(j)^4)/(1-z(j)^5), where z(j)=x^5^j.

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

EXAMPLE

From Hieronymus Fischer, May 30 2012: (Start)

a(1000) = 14889.

a(10^4) = 498889

a(10^5) = 11188889.

a(10^6) = 446888889. (End)

MATHEMATICA

Table[FromDigits/@Tuples[{1, 4, 6, 8, 9}, n], {n, 3}] // Flatten (* Vincenzo Librandi, Dec 17 2018 *)

PROG

(MAGMA) [n: n in [1..500] | Set(Intseq(n)) subset [1, 4, 6, 8, 9]]; // Vincenzo Librandi, Dec 17 2018

CROSSREFS

Cf. A046034 (numbers in which all digits are primes), A001742 (numbers in which all digits are noncomposites excluding 0), A202267 (numbers in which all digits are noncomposites), A084984 (numbers in which all digits are nonprimes), A029581 (numbers in which all digits are composites).

Cf. A084545, A001743, A001744, A014261, A014263.

Sequence in context: A067611 A190485 A105803 * A084985 A068631 A163520

Adjacent sequences:  A202265 A202266 A202267 * A202269 A202270 A202271

KEYWORD

nonn,base,easy

AUTHOR

Jaroslav Krizek, Dec 25 2011

STATUS

approved

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Last modified October 22 18:31 EDT 2019. Contains 328319 sequences. (Running on oeis4.)