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A280731 Lexicographically least strictly increasing sequence such that, for any n>0, Sum_{k=1..n} a(k) can be computed without carries in base 9 (the numbers are written in base 10).

%I A280731 #20 Feb 28 2022 17:33:36
%S A280731 1,2,3,9,10,18,19,81,90,162,171,729,810,1458,1539,6561,7290,13122,
%T A280731 13851,59049,65610,118098,124659,531441,590490,1062882,1121931,
%U A280731 4782969,5314410,9565938,10097379,43046721,47829690,86093442,90876411,387420489,430467210
%N A280731 Lexicographically least strictly increasing sequence such that, for any n>0, Sum_{k=1..n} a(k) can be computed without carries in base 9 (the numbers are written in base 10).
%C A280731 Base 9 analog of A278742.
%H A280731 Colin Barker, <a href="/A280731/b280731.txt">Table of n, a(n) for n = 1..1000</a>
%H A280731 N. J. A. Sloane, <a href="/A280731/a280731.jpg">Illustration of initial terms</a>
%H A280731 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,9).
%F A280731 For k>7, a(k+4) = 9*a(k).
%F A280731 G.f.: x*(1 + 2*x + 3*x^2 + 9*x^3 + x^4 - 8*x^6) / ((1 - 3*x^2)*(1 + 3*x^2)). - _Colin Barker_, Jan 10 2017
%t A280731 LinearRecurrence[{0,0,0,9},{1,2,3,9,10,18,19},50] (* _Harvey P. Dale_, Feb 28 2022 *)
%o A280731 (PARI) Vec(x*(1 + 2*x + 3*x^2 + 9*x^3 + x^4 - 8*x^6) / ((1 - 3*x^2)*(1 + 3*x^2)) + O(x^50)) \\ _Colin Barker_, Jan 10 2017
%Y A280731 Cf. A278742, A278743, A280051, A280052.
%Y A280731 See A281366 for these numbers written in base 9.
%K A280731 nonn,base,easy
%O A280731 1,2
%A A280731 _N. J. A. Sloane_, Jan 09 2017