A117597 Padovan numbers for which the sum of the digits is also a Padovan number.

0, 1, 2, 3, 4, 5, 7, 9, 12, 16, 21, 151, 200, 351, 4410, 73396, 170625, 922111, 1221537, 1618192, 2143648, 35676949, 62608681, 1380359512, 2422362079, 4250949112, 7459895657, 93722435101, 164471408185, 217878227876, 2066337330754

Offset

0,3

Links

Harvey P. Dale, Table of n, a(n) for n = 0..75

Example

The Padovan number 73396 is in the sequence because also 28 (=7+3+3+9+6) is a Padovan number.

Maple

p[0]:=1: p[1]:=1: p[2]:=1: for n from 3 to 170 do p[n]:=p[n-2]+p[n-3] od: P:=[seq(p[n], n=0..170)]: a:=proc(n) local nn, sod: nn:=convert(P[n], base, 10): sod:=add(nn[j], j=1..nops(nn)): if member(sod, P)=true then P[n] else fi end: 0, 1, seq(a(n), n=5..nops(P)); # Emeric Deutsch, Apr 16 2006

Mathematica

Join[{0}, With[{pads=LinearRecurrence[{0, 1, 1}, {1, 1, 1}, 150]}, Union[ Select[ pads, MemberQ[pads, Total[IntegerDigits[#]]]&]]]] (* Harvey P. Dale, Sep 05 2012 *)

Crossrefs

Cf. A000931.

Sequence in context: A164001 A117598 A120149 * A241336 A233522 A112639

Adjacent sequences: A117594 A117595 A117596 * A117598 A117599 A117600

Keyword

nonn,base

Author

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

Extensions

More terms from Emeric Deutsch, Apr 16 2006

Status

approved