A117600 Padovan numbers for which the multiplicative digital root is also a Padovan number.

0, 1, 2, 3, 4, 5, 7, 9, 12, 21, 37, 65, 114, 151, 200, 265, 351, 465, 1081, 1897, 2513, 3329, 4410, 5842, 10252, 13581, 17991, 31572, 41824, 55405, 73396, 128801, 170625, 226030, 299426, 396655, 525456, 696081, 1221537, 2143648, 2839729, 3761840, 4983377

Offset

1,3

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..2000

Maple

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

Mathematica

p=LinearRecurrence[{0, 1, 1}, {1, 0, 0}, 62]; Union[Select[p, MemberQ[p, NestWhile[Times@@IntegerDigits[#] &, #, # > 9 &]]&]] (* James C. McMahon, Sep 25 2024 *)

Crossrefs

Cf. A000931, A031347, A117598.

Sequence in context: A240840 A117599 A117602 * A117601 A117604 A117603

Adjacent sequences: A117597 A117598 A117599 * A117601 A117602 A117603

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