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 A014263 Numbers that contain even digits only. 41
 0, 2, 4, 6, 8, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 200, 202, 204, 206, 208, 220, 222, 224, 226, 228, 240, 242, 244, 246, 248, 260, 262, 264, 266, 268, 280, 282, 284, 286, 288, 400, 402, 404, 406, 408, 420, 422, 424 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The set of real numbers between 0 and 1 that contain no odd digits in their decimal expansion has Hausdorff dimension log 5 / log 10. Integers written in base 5 and then doubled (in base 10). - Franklin T. Adams-Watters, Mar 15 2006 A045888(a(n)) = 0. - Reinhard Zumkeller, Aug 25 2009 a(n) = A179082(n) for n <= 25. - Reinhard Zumkeller, Jun 28 2010 The carryless mod 10 "even" numbers (cf. A004529) sorted and duplicates removed. - N. J. A. Sloane, Aug 03 2010. Complement of A007957; A196564(a(n)) = 0; A103181(a(n)) = 0. - Reinhard Zumkeller, Oct 04 2011 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)=0,2,4,6,8 for k=0..4. - Hieronymus Fischer, Jun 03 2012 REFERENCES K. J. Falconer, The Geometry of Fractal Sets, Cambridge, 1985; p. 19. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA From Hieronymus Fischer, Jun 06 2012: (Start) a(n) = ((2*b_m(n)) mod 8 + 2)*10^m + sum_{j=0..m-1} ((2*b_j(n)) mod 10)*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) = 2*10^n. a(2*5^n+1) = 4*10^n. a(3*5^n+1) = 6*10^n. a(4*5^n+1) = 8*10^n. a(n) = 2*10^log_5(n-1) for n=5^k+1, a(n) < 2*10^log_5(n-1), else. a(n) > (8/9)*10^log_5(n-1) n>1. a(n) = 2*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)* (2+4x^5^j+ 6(x^2)^5^j+ 8(x^3)^5^j)/(1-x^5^(j+1)). Also: g(x) = 2*(x/(1-x))*sum_{j>=0} 10^j*x^5^j * (1-4x^(3*5^j)+3x^(4*5^j))/((1-x^5^j)(1-x^5^(j+1))). Also: g(x) = 2*(x/(1-x))*(h_(5,1)(x) + h_(5,2)(x) + h_(5,3)(x) + h_(5,4)(x) - 4*h_(5,5)(x)), where h_(5,k)(x) = sum_{j>=0} 10^j*(x^5^j)^k/(1-(x^5^j)^5). (End) a(5*n+i-4) = 10*a(n) + 2*i for n >= 1, i=0..4. - Robert Israel, Apr 07 2016 EXAMPLE a(1000) = 24888. a(10^4) = 60888. a(10^5) = 22288888. a(10^6) = 446888888. MAPLE a:= proc(m) local L, i;   L:= convert(m-1, base, 5);   2*add(L[i]*10^(i-1), i=1..nops(L)) end proc: seq(a(i), i=1..100); # Robert Israel, Apr 07 2016 MATHEMATICA Select[Range[450], And@@EvenQ[IntegerDigits[#]]&] (* Harvey P. Dale, Jan 30 2011 *) PROG (Haskell) a014263 n = a014263_list !! (n-1) a014263_list = filter (all (`elem` "02468") . show) [0, 2..] -- Reinhard Zumkeller, Jul 05 2011 (MAGMA) [n: n in [0..424] | Set(Intseq(n)) subset [0..8 by 2]];  // Bruno Berselli, Jul 19 2011 CROSSREFS Subsequence of A059708. Cf. A061810, A061811, A007091, A014261, A046034, A052382, A084544, A089581, A084984, A017042, A001743, A202267, A202268, A196563. Sequence in context: A179082 A194376 A062897 * A169906 A251853 A061651 Adjacent sequences:  A014260 A014261 A014262 * A014264 A014265 A014266 KEYWORD nonn,base,easy AUTHOR EXTENSIONS Examples and crossrefs added by Hieronymus Fischer, Jun 06 2012 STATUS approved

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Last modified April 20 06:19 EDT 2019. Contains 322294 sequences. (Running on oeis4.)