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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 FORMULA 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 *) PROG (PARI) is(n) = #setintersect(vecsort(digits(n), , 8), [1, 2, 3, 4, 5, 7])==0 \\ Felix Fröhlich, Sep 09 2019 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 EXTENSIONS Examples added by Hieronymus Fischer, May 30 2012 STATUS approved

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)