This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A278742 #32 Jan 10 2017 07:25:56
%S A278742 1,2,3,10,11,12,20,30,100,110,200,300,1000,1100,2000,2100,3000,10000,
%T A278742 20000,30000,100000,110000,120000,200000,300000,1000000,1100000,
%U A278742 2000000,3000000,10000000,11000000,20000000,21000000,30000000,100000000,200000000,300000000
%N A278742 Lexicographically least strictly increasing sequence such that, for any n>0, Sum_{k=1..n} a(k) can be computed without carries in base 10.
%H A278742 Colin Barker, <a href="/A278742/b278742.txt">Table of n, a(n) for n = 1..1000</a>
%H A278742 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10000).
%F A278742 a(n+17) = 10000*a(n) for any n>0.
%F A278742 a(17k+1) = 10^(4k), k >= 0. - _N. J. A. Sloane_, Jan 06 2017
%F A278742 G.f.: x*(1 +2*x +3*x^2 +10*x^3 +11*x^4 +12*x^5 +20*x^6 +30*x^7 +100*x^8 +110*x^9 +200*x^10 +300*x^11 +1000*x^12 +1100*x^13 +2000*x^14 +2100*x^15 +3000*x^16) / (1 -10000*x^17). - _Colin Barker_, Jan 10 2017
%e A278742 The first terms, alongside their partial sums, are:
%e A278742 n a(n) Partial sums (A280730)
%e A278742 -- ----- ----------------------
%e A278742 1 1 1
%e A278742 2 2 3
%e A278742 3 3 6
%e A278742 4 10 16
%e A278742 5 11 27
%e A278742 6 12 39
%e A278742 7 20 59
%e A278742 8 30 89
%e A278742 9 100 189
%e A278742 10 110 299
%e A278742 11 200 499
%e A278742 12 300 799
%e A278742 13 1000 1799
%e A278742 14 1100 2899
%e A278742 15 2000 4899
%e A278742 16 2100 6999
%e A278742 17 3000 9999
%e A278742 -- ----- -----
%e A278742 18 10000 19999
%e A278742 19 20000 39999
%e A278742 20 30000 69999
%t A278742 f[a_] := Function[w, Function[s, Total@ Map[PadLeft[#, s] &, w]]@ Max@ Map[Length, w]]@ Map[IntegerDigits, a]; g[n_] := FixedPoint[Function[k, If[Total@ Drop[RotateRight@ DigitCount@ k, 4] > 0, k + (6 * 10^(Position[#, 4][[1, 1]] - 1)) &@ Reverse@ IntegerDigits@ k, k]], n]; a = {1}; Do[If[n <= 17, k = g[Max@ a + 1]; While[Max@ f@ Join[a, {k}] > 9, k = g[k + 1]], k = 10^4 * a[[n - 17]]]; AppendTo[a, k], {n, 2, 37}]; a (* _Michael De Vlieger_, Dec 18 2016 *)
%o A278742 (PARI) a(n)=if(n>17, a(n-17)*10000, [1, 2, 3, 10, 11, 12, 20, 30, 100, 110, 200, 300, 1000, 1100, 2000, 2100, 3000][n]) \\ _Charles R Greathouse IV_, Nov 27 2016
%o A278742 (PARI) Vec(x*(1 +2*x +3*x^2 +10*x^3 +11*x^4 +12*x^5 +20*x^6 +30*x^7 +100*x^8 +110*x^9 +200*x^10 +300*x^11 +1000*x^12 +1100*x^13 +2000*x^14 +2100*x^15 +3000*x^16) / (1 -10000*x^17) + O(x^50)) \\ _Colin Barker_, Jan 10 2017
%Y A278742 Cf. A278743, A279732, A280730.
%K A278742 nonn,base,easy
%O A278742 1,2
%A A278742 _Rémy Sigrist_, Nov 27 2016