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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. 7
1, 2, 3, 10, 11, 12, 20, 30, 100, 110, 200, 300, 1000, 1100, 2000, 2100, 3000, 10000, 20000, 30000, 100000, 110000, 120000, 200000, 300000, 1000000, 1100000, 2000000, 3000000, 10000000, 11000000, 20000000, 21000000, 30000000, 100000000, 200000000, 300000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,10000).

FORMULA

a(n+17) = 10000*a(n) for any n>0.

a(17k+1) = 10^(4k), k >= 0. - N. J. A. Sloane, Jan 06 2017

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

EXAMPLE

The first terms, alongside their partial sums, are:

n     a(n)     Partial sums (A280730)

--    -----    ----------------------

1         1              1

2         2              3

3         3              6

4        10             16

5        11             27

6        12             39

7        20             59

8        30             89

9       100            189

10      110            299

11      200            499

12      300            799

13     1000           1799

14     1100           2899

15     2000           4899

16     2100           6999

17     3000           9999

--    -----          -----

18    10000          19999

19    20000          39999

20    30000          69999

MATHEMATICA

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 *)

PROG

(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

(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

CROSSREFS

Cf. A278743, A279732, A280730.

Sequence in context: A212067 A060811 A146327 * A250174 A285622 A081706

Adjacent sequences:  A278739 A278740 A278741 * A278743 A278744 A278745

KEYWORD

nonn,base,easy

AUTHOR

Rémy Sigrist, Nov 27 2016

STATUS

approved

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Last modified September 18 03:39 EDT 2020. Contains 337164 sequences. (Running on oeis4.)