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A003893 a(n) = Fibonacci(n) mod 10. 33
0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3, 0, 3, 3, 6, 9, 5, 4, 9, 3, 2, 5, 7, 2, 9, 1, 0, 1, 1, 2, 3, 5, 8, 3, 1, 4, 5, 9, 4, 3, 7, 0, 7, 7, 4, 1, 5, 6, 1, 7, 8, 5, 3, 8, 1, 9, 0, 9, 9, 8, 7, 5, 2, 7, 9, 6, 5, 1, 6, 7, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
All blocks of 60 successive terms contain 20 even and 40 odd numbers. - Reinhard Zumkeller, Apr 09 2005
These are the analogs of the Fibonacci numbers in carryless arithmetic mod 10.
REFERENCES
G. Marsaglia, The mathematics of random number generators, pp. 73-90 of S. A. Burr, ed., The Unreasonable Effectiveness of Number Theory, Proc. Sympos. Appl. Math., 46 (1992). Amer. Math. Soc.
LINKS
David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.
H. S. M. Coxeter, The Golden Section, Phyllotaxis and Wythoff's Game, Scripta Math. 19 (1953), 135-143. [Annotated scanned copy]
Gregory P. Dresden, Three transcendental numbers from the last non-zero digits of n^n, F_n and n!, Math. Mag., pp. 96-105, vol. 81, 2008.
Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1, 0, 0, 1, 0, 0, -1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1).
FORMULA
Periodic with period 60 = A001175(10).
From Reinhard Zumkeller, Apr 09 2005: (Start)
a(n) = (a(n-1) + a(n-2)) mod 10 for n > 1, a(0) = 0, a(1) = 1.
a(n) = A105471(n) - A105472(n)*10 = A105471(n)/10. (End)
a(n) = A010879(A000045(n)). - Michel Marcus, Nov 19 2022
MAPLE
with(combinat, fibonacci); A003893 := proc(n) fibonacci(n) mod 10; end;
MATHEMATICA
Table[Mod[Fibonacci[n], 10], {n, 0, 99}] (* Alonso del Arte, Jul 29 2013 *)
Table[IntegerDigits[Fibonacci[n]][[-1]], {n, 0, 99}] (* Alonso del Arte, Jul 29 2013 *)
NumberDigit[Fibonacci[Range[0, 120]], 0] (* Requires Mathematica version 12 or later *) (* Harvey P. Dale, Jul 05 2021 *)
PROG
(Haskell)
a003893 n = a003893_list !! n
a003893_list = 0 : 1 : zipWith (\u v -> (u + v) `mod` 10)
(tail a003893_list) a003893_list
-- Reinhard Zumkeller, Jul 01 2013
(PARI) a(n)=fibonacci(n)%10 \\ Charles R Greathouse IV, Feb 03 2014
(Magma) [Fibonacci(n) mod 10: n in [0..100]]; // Vincenzo Librandi, Feb 04 2014
(Python)
A003893_list, a, b, = [], 0, 1
for _ in range(10**3):
A003893_list.append(a)
a, b = b, (a+b) % 10 # Chai Wah Wu, Nov 26 2015
CROSSREFS
Sequence in context: A362358 A096320 A105955 * A152303 A064737 A246558
KEYWORD
nonn,base,easy
AUTHOR
N. J. A. Sloane, elipper(AT)uoft02.utoledo.edu
EXTENSIONS
More terms from Ray Chandler, Nov 15 2003
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)