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%I #6 Sep 03 2017 11:24:38
%S 0,1,2,3,4,5,7,9,12,21,37,65,114,151,200,265,351,465,1081,1897,2513,
%T 3329,4410,5842,10252,13581,17991,31572,41824,55405,73396,128801,
%U 170625,226030,299426,396655,525456,696081,1221537,2143648,2839729,3761840,4983377
%N Padovan numbers for which the multiplicative digital root is also a Padovan number.
%H Nathaniel Johnston, <a href="/A117600/b117600.txt">Table of n, a(n) for n = 1..2000</a>
%p Padovan := proc(n) option remember: if(n=0)then return 1:elif(n<=2)then return 0:fi: return procname(n-3) + procname(n-2): end: MultDig := proc(n) return mul(d, d=convert(n, base, 10)): end: MultRoot := proc(n) local m: m:=n: while(length(m)>1)do m:=MultDig(m): od: return m: end: A117600ind := proc(n) option remember: local k: if(n=1)then return 4:fi: for k from procname(n-1)+1 do if(not Padovan(k)=Padovan(procname(n-1)) and MultRoot(Padovan(k)) in {0,1,2,3,4,5,7,9})then return k: fi: od: end: seq(Padovan(A117600ind(n)), n=1..60); # _Nathaniel Johnston_, May 05 2011
%Y Cf. A000931, A031347.
%K nonn,easy,base
%O 1,3
%A Luc Stevens (lms022(AT)yahoo.com), Apr 05 2006
%E Offset changed from 0 to 1 by _Nathaniel Johnston_, May 05 2011
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