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A117602
Padovan numbers which can be divided by their digital root.
1
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
1,2
LINKS
Kevin Ryde, PARI/GP Code, finding linear recurrence and g.f.
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
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 *)
PROG
(PARI) \\ See links.
CROSSREFS
KEYWORD
nonn,easy,base
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 05 2006
EXTENSIONS
Offset changed from 0 to 1 by Nathaniel Johnston, May 05 2011
STATUS
approved