A117766 Fibonacci numbers for which the sum of the digits is a Lucas number.

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

Offset

0,2

Comments

The next term has 108 digits. - Harvey P. Dale, Apr 08 2018

Links

Table of n, a(n) for n=0..10.

Example

196418 is in the sequence because (1) it is a Fibonacci number and (2)the sum of its digits 1+9+6+4+1+8=29 is a Lucas number.

Maple

with(combinat): L[1]:=1:L[2]:=3: for m from 3 to 30 do L[m]:=L[m-1]+L[m-2] od: LL:=[seq(L[m], m=1..30)]: a:=proc(n) local ff, sod: ff:=convert(fibonacci(n), base, 10): sod:=add(ff[j], j=1..nops(ff)): if member(sod, LL)=true then fibonacci(n) else fi end: seq(a(n), n=2..450); # Emeric Deutsch, Apr 16 2006

Mathematica

Module[{nn=600, luc}, luc=LucasL[Range[nn]]; Select[Fibonacci[ Range[ 2, nn]], MemberQ[luc, Total[ IntegerDigits[#]]]&]] (* Harvey P. Dale, Apr 08 2018 *)

Crossrefs

Cf. A000045, A000204.

Sequence in context: A145024 A055059 A050903 * A243162 A147351 A147097

Adjacent sequences: A117763 A117764 A117765 * A117767 A117768 A117769

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 15 2006

Extensions

Corrected and extended by Emeric Deutsch, Apr 16 2006

Status

approved