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 A029581 All digits are composite. 10
 4, 6, 8, 9, 44, 46, 48, 49, 64, 66, 68, 69, 84, 86, 88, 89, 94, 96, 98, 99, 444, 446, 448, 449, 464, 466, 468, 469, 484, 486, 488, 489, 494, 496, 498, 499, 644, 646, 648, 649, 664, 666, 668, 669, 684, 686, 688, 689, 694, 696, 698, 699, 844, 846, 848 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS If n is represented as a zerofree base-4 number (see A084544) according to n=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)=4,6,8,9 for k=1..4. - Hieronymus Fischer, May 30 2012 LINKS Hieronymus Fischer, Table of n, a(n) for n = 1..10000 FORMULA From Hieronymus Fischer, May 30 and Jun 25 2012: (Start) a(n) = Sum_{j=0..m-1} (2*b(j) mod 8 + 4 + floor(b(j)/4) - floor((b(j)+1)/4))*10^j, where m = floor(log_4(3*n+1)), b(j) = floor((3*n+1-4^m)/(3*4^j)). Also: a(n) = Sum_{j=0..m-1} (A010877(2*b(j)) + 4 + A002265(b(j)) - A002265(b(j)+1))*10^j. Special values: a(1*(4^n-1)/3) = 4*(10^n-1)/9. a(2*(4^n-1)/3) = 2*(10^n-1)/3. a(3*(4^n-1)/3) = 8*(10^n-1)/9. a(4*(4^n-1)/3) = 10^n-1. a(n) < 4*(10^log_4(3*n+1)-1)/9, equality holds for n=(4^k-1)/3, k > 0. a(n) < 4*A084544(n), equality holds iff all digits of A084544(n) are 1. a(n) > 2*A084544(n). Lower and upper limits: lim inf a(n)/10^log_4(n) = 1/10*10^log_4(3) = 0.62127870, for n --> inf. lim sup a(n)/10^log_4(n) = 4/9*10^log_4(3) = 2.756123868970, for n --> inf. where 10^log_4(n) = n^1.66096404744... G.f.: g(x) = (x^(1/3)*(1-x))^(-1) Sum_{j>=0} 10^j*z(j)^(4/3)*(1-z(j))*(4 + 6z(j) + 8*z(j)^2 + 9*z(j)^3)/(1-z(j)^4), where z(j) = x^4^j. Also: g(x) = (1/(1-x))*(4*h_(4,0)(x) + 2*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+1)-1)/3)*(x^(k*4^j)/(1-x^4^(j+1)). (End) EXAMPLE From Hieronymus Fischer, May 30 2012: (Start) a(1000) = 88649. a(10^4) = 6468989 a(10^5) = 449466489. (End) MATHEMATICA Table[FromDigits/@Tuples[{4, 6, 8, 9}, n], {n, 3}] // Flatten (* Vincenzo Librandi, Dec 17 2018 *) PROG (MAGMA) [n: n in [1..1000] | Set(Intseq(n)) subset [4, 6, 8, 9]]; // Vincenzo Librandi, Dec 17 2018 CROSSREFS Cf. A002808, A001744, A046034, A084544, A084984, A017042, A001743, A014261, A014263, A202267, A202268. Sequence in context: A001744 A113624 A113591 * A202262 A202266 A232541 Adjacent sequences:  A029578 A029579 A029580 * A029582 A029583 A029584 KEYWORD nonn,base AUTHOR EXTENSIONS Offset corrected by Arkadiusz Wesolowski, Oct 03 2011 STATUS approved

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Last modified November 28 06:42 EST 2021. Contains 349401 sequences. (Running on oeis4.)