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

Author

N. J. A. Sloane, Jan 09 2017

Keywords

• nonn
• base
• easy

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).

Crossrefs

Cf. A278742, A278743, A280051, A280052.

See A281366 for these numbers written in base 9.

Programs

Mathematica

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

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

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