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 A037314 Numbers n such that (sum of base 3 digits of n)=(sum of base 9 digits of n). 13
 0, 1, 2, 9, 10, 11, 18, 19, 20, 81, 82, 83, 90, 91, 92, 99, 100, 101, 162, 163, 164, 171, 172, 173, 180, 181, 182, 729, 730, 731, 738, 739, 740, 747, 748, 749, 810, 811, 812, 819, 820, 821, 828, 829, 830, 891, 892, 893, 900, 901, 902, 909, 910, 911 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) = Sum{d(i)*9^i: i=0,1,...,m}, where Sum{d(i)*3^i: i=0,1,...,m} is the base 3 representation of n. Numbers that can be written using only digits 0, 1 and 2 in base 9. Also, write n in base 3, read as base 9: (3) [n] (9) in base change notation. a(3n+k) = 9a(n)+k for k in {0,1,2}. - Franklin T. Adams-Watters, Jul 24 2006 LINKS FORMULA G.f. f(x) = sum(j>=0, 9^j*x^(3^j)*(1+x^(3^j)-2*x^(2*3^j))/((1-x)*(1-x^(3^(j+1))))) satisfies f(x) = 9*(x^2+x+1)*f(x^3) + x*(1+2*x)/(1-x^3). - Robert Israel, Apr 13 2015 MATHEMATICA Table[FromDigits[RealDigits[n, 3], 9], {n, 1, 100}] (* Clark Kimberling, Aug 14 2012 *) Select[Range[0, 1000], Total[IntegerDigits[#, 3]]==Total[IntegerDigits[#, 9]]&] (* Harvey P. Dale, Feb 17 2020 *) PROG (PARI) a(n) = {my(d = digits(n, 3)); subst(Pol(d), x, 9); } \\ Michel Marcus, Apr 09 2015 CROSSREFS Cf. A007089, A208665, A338086 (ternary digit duplication). Cf. A053735, A053830. Sequence in context: A135782 A281899 A037457 * A226841 A218560 A031443 Adjacent sequences:  A037311 A037312 A037313 * A037315 A037316 A037317 KEYWORD nonn,base,changed AUTHOR EXTENSIONS Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007 Offset changed to 0 by Clark Kimberling, Aug 14 2012 STATUS approved

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Last modified October 22 10:18 EDT 2020. Contains 337950 sequences. (Running on oeis4.)