A244923 Numbers n such that the digit sum of Fibonacci(n) is equal to the digit sum of Lucas(n).

1, 13, 61, 73, 97, 217, 349, 649, 937, 1477, 1513, 1729, 2005, 2077, 2209, 3265, 3649, 3889, 4093, 4609, 4945, 5497, 5749, 5929, 6109, 7309, 7441, 8041, 8389, 8821, 9925, 10525, 10669, 11605, 13201, 13345, 16021, 18529, 18649, 20293, 21481, 22573, 22729, 24169

Offset

1,2

Comments

Numbers n such that A004090(n) = A139374(n).

Subsequence of A017533.

It seems that n is odd. The primes of the sequence are: 13, 61, 73, 97, 349, 937, 3889, 4093, 5749, 7309, 8389, 8821, 21481, 22573, 24169, ...

Fibonacci(j) == Lucas(j) (mod 9) iff j == 1 (mod 12), so all a(n) == 1 (mod 12). - Robert Israel, Jul 10 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..95

Example

13 is in the sequence because Fibonacci(13) = 233, Lucas(13) = 521 and 2+3+3 = 5+2+1 = 8.

Mathematica

lst={}; Table[If[Total[IntegerDigits[LucasL[n]]] == Total[IntegerDigits[Fibonacci[n]]], AppendTo[lst, n]], {n, 0, 25000}]; lst
Select[Range[25000], Total[IntegerDigits[Fibonacci[#]]]==Total[IntegerDigits[LucasL[#]]]&] (* Harvey P. Dale, Mar 31 2024 *)

Crossrefs

Cf. A000032, A000045, A004090, A017533, A139374.

Sequence in context: A304542 A228558 A316550 * A146764 A336794 A145474

Adjacent sequences: A244920 A244921 A244922 * A244924 A244925 A244926

Keyword

nonn,base

Author

Michel Lagneau, Jul 08 2014

Status

approved