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).

1, 2, 3, 9, 10, 18, 19, 81, 90, 162, 171, 729, 810, 1458, 1539, 6561, 7290, 13122, 13851, 59049, 65610, 118098, 124659, 531441, 590490, 1062882, 1121931, 4782969, 5314410, 9565938, 10097379, 43046721, 47829690, 86093442, 90876411, 387420489, 430467210

Offset

1,2

Comments

Base 9 analog of A278742.

Links

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

N. J. A. Sloane, Illustration of initial terms

Index entries for linear recurrences with constant coefficients, signature (0,0,0,9).

Formula

For k>7, a(k+4) = 9*a(k).

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

Mathematica

LinearRecurrence[{0, 0, 0, 9}, {1, 2, 3, 9, 10, 18, 19}, 50] (* Harvey P. Dale, Feb 28 2022 *)

Prog

(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

Crossrefs

Cf. A278742, A278743, A280051, A280052.

See A281366 for these numbers written in base 9.

Sequence in context: A030743 A098020 A047358 * A353614 A352198 A003140

Adjacent sequences: A280728 A280729 A280730 * A280732 A280733 A280734

Keyword

nonn,base,easy

Author

N. J. A. Sloane, Jan 09 2017

Status

approved