A117959 Perrin numbers which are divisible by their digital root.

2, 3, 5, 7, 10, 12, 39, 90, 486, 1130, 1497, 1983, 3480, 4610, 10717, 24914, 33004, 57918, 76725, 134643, 178364, 549289, 727653, 1691588, 2240877, 2968530, 3932465, 5209407, 12110402, 28153269, 65448410, 86700684, 114853953, 1089264462, 1911525877, 3354494070

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), May 03 2006

Keywords

• base
• nonn

Examples

			1130 is in the sequence because (1) it is a Perrin number, (2) the digital root is 5 and (3) 1130 is divisible by 5.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3698

Crossrefs

Intersection of A001608 and A064807.

Cf. A010888.

Programs

Maple

R:= NULL: count:= 0:
a:= 3: b:= 0: c:= 2:
while count < 100 do
  q:= a+b;
  a:= b; b:= c; c:= q;
  dr:= c mod 9; if dr = 0 then dr:= 9 fi;
  if c mod dr = 0 then R:= R,c; count:= count+1;
  fi
od:
sort(convert({R},list)); # Robert Israel, Mar 16 2023

Mathematica

Select[Union @ LinearRecurrence[{0, 1, 1}, {2, 3, 2}, 100], Divisible[#, Mod[# - 1, 9] + 1] &] (* Amiram Eldar, Feb 06 2021 *)

Extensions

Data corrected by Amiram Eldar, Feb 06 2021