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

Author

Benoit Cloitre, Aug 07 2002

Keywords

• nonn
• base
• easy

Comments

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

Links

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

Crossrefs

Cf. A000045, A003893.

Programs

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 *)

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