A117602 Padovan numbers which can be divided by their digital root.

1, 2, 3, 4, 5, 7, 9, 12, 21, 28, 37, 114, 200, 351, 616, 816, 1081, 1432, 1897, 4410, 5842, 10252, 13581, 17991, 23833, 31572, 41824, 55405, 73396, 170625, 396655, 525456, 696081, 1221537, 1618192, 2143648, 3761840, 11584946, 20330163, 26931732, 62608681

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 05 2006

Keywords

• nonn
• easy
• base

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..1000
• Kevin Ryde, PARI/GP Code, finding linear recurrence and g.f.
• Index entries for linear recurrences with constant coefficients, order 8544.

Crossrefs

Cf. A000931, A117601, A117603, A117604.

Programs

Maple

A000931 := proc(n) option remember: if(n=0)then return 1: elif(n<=2)then return 0: else return procname(n-2)+procname(n-3): fi: end: A117602ind := proc(n) option remember: local k,p: if(n=1)then return 7: fi: for k from procname(n-1)+1 do p:=A000931(k): if(not p=A000931(A117602ind(n-1)) and p mod (((p-1) mod 9) + 1) = 0)then return k: fi: od: end: seq(A000931(A117602ind(n)),n=1..41); # Nathaniel Johnston, May 05 2011

Mathematica

p=LinearRecurrence[{0, 1, 1}, {1, 0, 0}, 71];Rest[Union[Select[p,Divisible[#,Mod[#-1,9]+1]&]]] (* James C. McMahon, Sep 25 2024 *)

PARI

\\ See links.

Formula

a(n) = X*a(n-s) + Y*a(n-2*s) + a(n-3*s) for n >= 8546, where s = 2848, X = Perrin(f) = A001608(f), Y = -Perrin(-f) = A078712(f), f = 4368. - Kevin Ryde, Oct 12 2024

Extensions

Offset changed from 0 to 1 by Nathaniel Johnston, May 05 2011