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A001743 Every digit contains at least one loop (version 1). 23
0, 6, 8, 9, 60, 66, 68, 69, 80, 86, 88, 89, 90, 96, 98, 99, 600, 606, 608, 609, 660, 666, 668, 669, 680, 686, 688, 689, 690, 696, 698, 699, 800, 806, 808, 809, 860, 866, 868, 869, 880, 886, 888, 889, 890, 896, 898, 899, 900, 906, 908, 909, 960, 966, 968, 969 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

See A001744 for the other version.

If n-1 is represented as a base-4 number (see A007090) 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)=0,6,8,9 for k=0..3. - Hieronymus Fischer, May 30 2012

LINKS

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

Index entries for 10-automatic sequences.

FORMULA

Contribution from Hieronymus Fischer, May 30 2012 (Start):

a(n) = ((b_m(n)+6) mod 9 + floor((b_m(n)+2)/3) - floor(b_m(n)/3))*10^m + sum_{j=0..m-1} (b_j(n) mod 4 +5*floor((b_j(n)+3)/4) +floor((b_j(n)+2)/4)- 6*floor(b_j(n)/4)))*10^j, where n>1, b_j(n)) = floor((n-1-4^m)/4^j), m = floor(log_4(n-1)).

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

a(2*4^n+1) = 8*10^n.

a(3*4^n+1) = 9*10^n.

a(n) = 6*10^log_4(n-1) for n=4^k+1,

a(n) < 6*10^log_4(n-1), else.

a(n) > 10^log_4(n-1) for n>1.

a(n) = 6*A007090(n-1), iff the digits of A007090(n-1) are 0 or 1.

G.f.: g(x) = (x/(1-x))*sum_{j>=0} 10^j*x^4^j *(1-x^4^j)* (6 + 8x^4^j + 9(x^2)^4^j)/(1-x^4^(j+1)).

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

EXAMPLE

a(1000) = 99896.

a(10^4) = 8690099.

a(10^5) = 680688699.

MATHEMATICA

Union[Flatten[Table[FromDigits/@Tuples[{0, 6, 8, 9}, n], {n, 3}]]] (* Harvey P. Dale, Sep 04 2013 *)

CROSSREFS

Cf. A007090, A046034, A029581, A084984, A017042, A001744, A014261, A014263, A202267, A202268.

Sequence in context: A284990 A238621 A099102 * A256964 A046344 A116366

Adjacent sequences:  A001740 A001741 A001742 * A001744 A001745 A001746

KEYWORD

base,nonn,easy

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Examples added by Hieronymus Fischer, May 30 2012

STATUS

approved

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)