A072683 Numbers k such that the last digit of F(k) is 3 where F(k) is the k-th Fibonacci number.

4, 7, 13, 26, 44, 46, 47, 53, 64, 67, 73, 86, 104, 106, 107, 113, 124, 127, 133, 146, 164, 166, 167, 173, 184, 187, 193, 206, 224, 226, 227, 233, 244, 247, 253, 266, 284, 286, 287, 293, 304, 307, 313, 326, 344, 346, 347, 353, 364, 367, 373, 386, 404, 406, 407

Offset

1,1

Comments

Numbers that are congruent to {4, 7, 13, 26, 44, 46, 47, 53} mod 60. - Amiram Eldar, Jan 01 2022

Links

Table of n, a(n) for n=1..55.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,1,-1).

Formula

G.f.: x*(7*x^8+6*x^7+x^6+2*x^5+18*x^4+13*x^3+6*x^2+3*x+4) / ((1-x)^2*(1+x)*(1+x^2)*(1+x^4)). - Colin Barker, Jun 16 2013

a(n) ~ 15*n/2. - Stefano Spezia, Jul 09 2023

Mathematica

Select[Range[500], Mod[Fibonacci[#], 10]==3&] (* Harvey P. Dale, Jan 24 2012 *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 1, -1}, {4, 7, 13, 26, 44, 46, 47, 53, 64}, 60] (* Harvey P. Dale, Apr 10 2022 *)

Crossrefs

Cf. A000045, A003893.

Sequence in context: A004119 A074864 A074865 * A304004 A293342 A298346

Adjacent sequences: A072680 A072681 A072682 * A072684 A072685 A072686

Keyword

nonn,base,easy

Author

Benoit Cloitre, Aug 07 2002

Status

approved