A130877 Numbers that are congruent to {0, 5} mod 9.

0, 5, 9, 14, 18, 23, 27, 32, 36, 41, 45, 50, 54, 59, 63, 68, 72, 77, 81, 86, 90, 95, 99, 104, 108, 113, 117, 122, 126, 131, 135, 140, 144, 149, 153, 158, 162, 167, 171, 176, 180, 185, 189, 194, 198, 203, 207, 212, 216, 221, 225, 230, 234, 239, 243, 248, 252, 257

Offset

1,2

Comments

Numbers m such that m = digitsum(k*(m+k)) for some k>=0.

The first differences are 2-periodic: 5, 4, 5, 4, etc. The minimum numbers k associated to the first elements of the sequence are (m,k): (0,0), (5,2), (9,3), (14,5), (18,15), (23,44), (27,42), (32,119), etc.

Links

Table of n, a(n) for n=1..58.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = a(n-2) + 9 for n >= 3.

a(n) = 9/2*(n+1) - 4 + Sum{j=0..n} (-1)^j/2.

O.g.f.: x^2(5+4x)/((1+x)(1-x)^2). a(n) = 9(n-1)/2+(1+(-1)^n)/4. - R. J. Mathar, Jun 13 2008

a(n+1) = Sum_{k>=0} A030308(n,k)*A116453(k+1). - Philippe Deléham, Oct 17 2011

a(n) = 5n - 5 - floor((n-1)/2). - Wesley Ivan Hurt, Oct 25 2013

Maple

op(select(n->n mod 9=0 or n mod 9=5, [$0..257])); # Paolo P. Lava, Jul 12 2018

Mathematica

Table[5n-5-Floor[(n-1)/2], {n, 100}] (* Wesley Ivan Hurt, Oct 25 2013 *)
Select[Range[0, 300], MemberQ[{0, 5}, Mod[#, 9]]&] (* or *) LinearRecurrence[ {1, 1, -1}, {0, 5, 9}, 60] (* Harvey P. Dale, Aug 04 2019 *)

Prog

(PARI) forstep(n=0, 200, [5, 4], print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

Crossrefs

Cf. A008591, A017221.

Sequence in context: A314834 A314835 A314836 * A314837 A314838 A314839

Adjacent sequences: A130874 A130875 A130876 * A130878 A130879 A130880

Keyword

nonn,easy

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 25 2007

Status

approved