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 A001744 Numbers n such that every digit contains a loop (version 2). 24
 0, 4, 6, 8, 9, 40, 44, 46, 48, 49, 60, 64, 66, 68, 69, 80, 84, 86, 88, 89, 90, 94, 96, 98, 99, 400, 404, 406, 408, 409, 440, 444, 446, 448, 449, 460, 464, 466, 468, 469, 480, 484, 486, 488, 489, 490, 494, 496, 498, 499, 600, 604, 606, 608, 609, 640, 644, 646 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS See A001743 for the other version. If n-1 is represented as a base-5 number (see A007091) 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)=0,4,6,8,9 for k=0..4. - 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) = ((2*b_m(n)) mod 8 + 4 + floor(b_m(n)/4) - floor((b_m(n)+1)/4))*10^m + sum_{j=0..m-1} ((2*b_j(n))) mod 10 + 2*floor((b_j(n)+4)/5) - floor((b_j(n)+1)/5) -floor(b_j(n)/5)))*10^j, where n>1, b_j(n)) = floor((n-1-5^m)/5^j), m = floor(log_5(n-1)). a(1*5^n+1) = 4*10^n. a(2*5^n+1) = 6*10^n. a(3*5^n+1) = 8*10^n. a(4*5^n+1) = 9*10^n. a(n) = 4*10^log_5(n-1) for n=5^k+1, a(n) < 4*10^log_5(n-1), otherwise. a(n) > 10^log_5(n-1) n>1. a(n) = 4*A007091(n-1), iff the digits of A007091(n-1) are 0 or 1. G.f.: g(x) = (x/(1-x))*sum_{j>=0} 10^j*x^5^j*(1-x^5^j)*(4 + 6x^5^j + 8(x^2)^5^j + 9(x^3)^5^j)/(1-x^5^(j+1)). Also: g(x) = (x/(1-x))*(4*h_(5,1)(x) + 2*h_(5,2)(x) + 2*h_(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)^k/(1-(x^5^j)^5). (End) EXAMPLE a(1000) = 46999. a(10^4) = 809999. a(10^5) = 44499999. a(10^6) = 668999999. MATHEMATICA FromDigits/@Tuples[{0, 4, 6, 8, 9}, 3] (* Harvey P. Dale, Aug 16 2018 *) PROG (PARI) is(n) = #setintersect(vecsort(digits(n), , 8), [1, 2, 3, 5, 7])==0 \\ Felix FrÃ¶hlich, Sep 09 2019 CROSSREFS Cf. A061371, A029581, A007091, A046034, A084544, A084984, A017042, A001743, A014261, A014263, A202267, A202268. Sequence in context: A156673 A073866 A202260 * A113624 A113591 A029581 Adjacent sequences:  A001741 A001742 A001743 * A001745 A001746 A001747 KEYWORD base,nonn,easy AUTHOR EXTENSIONS Ambiguous comment deleted by Zak Seidov, May 25 2010 Examples added by Hieronymus Fischer, May 30 2012 STATUS approved

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Last modified August 9 00:15 EDT 2022. Contains 356016 sequences. (Running on oeis4.)