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Fibonacci numbers for which the sum of the digits is a Lucas number.
1

%I #8 Apr 08 2018 16:18:02

%S 1,3,13,21,34,610,196418,1134903170,20365011074,

%T 15635695580168194910579363790217849593217,

%U 1049252690665646467530632231274619718410203796555123147644873726135009824265250

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

%C The next term has 108 digits. - _Harvey P. Dale_, Apr 08 2018

%e 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.

%p 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

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

%Y Cf. A000045, A000204.

%K base,nonn

%O 0,2

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

%E Corrected and extended by _Emeric Deutsch_, Apr 16 2006