A139563 Fibonacci numbers whose digit sum is a Lucas number.

1, 2, 3, 13, 21, 34, 610, 196418, 1134903170, 20365011074, 15635695580168194910579363790217849593217, 1049252690665646467530632231274619718410203796555123147644873726135009824265250

Offset: 1

Author

Parthasarathy Nambi, Jun 11 2008

Keywords

• nonn
• base
• less

Comments

Depending on whether the Lucas numbers are defined by A000032 or by A000204, one obtains this sequence here or A117766. - R. J. Mathar, Nov 03 2008

The next term (a(13)) has 108 digits. - Harvey P. Dale, Jul 01 2022

Examples

			196418 is a Fibonacci number whose digit sum 29 is a Lucas number.
		

Crossrefs

Cf. A000032, A000045, A004090, A117766.

Programs

Mathematica

luQ[n_] := n==2 || Block[{i=1}, While[LucasL[i] < n, i++]; LucasL[i] == n]; Select[
Fibonacci[ Range[2, 400]], luQ[ Plus @@ IntegerDigits[#]] &] (* Giovanni Resta, Mar 15 2020 *)
Module[{nn=500,ln=LucasL[Range[0,20]]},Select[Fibonacci[Range[nn]],MemberQ[ ln,Total[ IntegerDigits[ #]]]&]]//Union (* Harvey P. Dale, Jul 01 2022 *)

Extensions

1 added in front by R. J. Mathar, Nov 03 2008

More terms from Jinyuan Wang, Mar 15 2020