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
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.
Programs
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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
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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