A072702 Last digit of F(n) is 4 where F(n) is the n-th Fibonacci number.

9, 12, 18, 51, 69, 72, 78, 111, 129, 132, 138, 171, 189, 192, 198, 231, 249, 252, 258, 291, 309, 312, 318, 351, 369, 372, 378, 411, 429, 432, 438, 471, 489, 492, 498, 531, 549, 552, 558, 591, 609, 612, 618, 651, 669, 672, 678, 711, 729, 732, 738, 771, 789

Offset

1,1

Comments

Sequence contains numbers of form (9+60k), (12+60k), (18+60k), (51+60k), with k>=0.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

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

Formula

G.f.: x*(9*x^4+33*x^3+6*x^2+3*x+9) / (x^5-x^4-x+1). - Colin Barker, Jun 16 2013

a(n) = (-60 + 6*(-1)^n + (9+21*i)*(-i)^n + (9-i*21)*i^n + 60*n) / 4 where i=sqrt(-1). - Colin Barker, Oct 16 2015

Mathematica

With[{fibs=Fibonacci[Range[800]]}, Flatten[Position[fibs, _?(Last[ IntegerDigits[ #]]==4&)]]] (* Harvey P. Dale, Sep 24 2012 *)
Position[Mod[Fibonacci[Range[800]], 10], 4]//Flatten (* Harvey P. Dale, Apr 09 2023 *)

Prog

(PARI) a(n) = (-60 + 6*(-1)^n + (9+21*I)*(-I)^n + (9-I*21)*I^n + 60*n) / 4 \\ Colin Barker, Oct 16 2015
(PARI) Vec(x*(9*x^4+33*x^3+6*x^2+3*x+9)/(x^5-x^4-x+1) + O(x^100)) \\ Colin Barker, Oct 16 2015
(PARI) for(n=0, 1e3, if(fibonacci(n) % 10 == 4, print1(n", "))) \\ Altug Alkan, Oct 16 2015

Crossrefs

Cf. A000045, A003893.

Sequence in context: A162822 A087269 A153973 * A357185 A366865 A366861

Adjacent sequences: A072699 A072700 A072701 * A072703 A072704 A072705

Keyword

nonn,base,easy

Author

Benoit Cloitre, Aug 07 2002

Status

approved