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A003893
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Fibonacci(n) mod 10.
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24
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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; internal format)
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OFFSET
| 0,4
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COMMENTS
| All blocks of 60 successive terms contain 20 even and 40 odd numbers. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 09 2005
These are the analogs of the Fibonacci numbers in carryless arithmetic mod 10.
a(n) = A105471(n) - A105472(n)*10 = A105471(n)/10. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 09 2005
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REFERENCES
| Gregory P. Dresden, "Three transcendental numbers from the last non-zero digits of n^n, F_n and n!", 'Mathematics Magazine', pp. 96-105, vol. 81, 2008.
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.
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LINKS
| David Applegate, Marc LeBrun and N. J. A. Sloane, Carryless Arithmetic (I): The Mod 10 Version.
R. Knott, Mathematics of the Fibonacci Series
Index entries for sequences related to final digits of numbers
Index entries for sequences related to carryless arithmetic
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FORMULA
| Periodic with period 60.
a(n) = (a(n-1) + a(n-2)) mod 10 for n>1, a(0) = 0, a(1) = 1. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 09 2005
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MAPLE
| with(combinat, fibonacci); A003893 := proc(n) fibonacci(n) mod 10; end;
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MATHEMATICA
| Table[f=Fibonacci[n]; Mod[f, 10], {n, 0, 30}] (Vladimir Orlovsky, Jul 21 2008)
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CROSSREFS
| Cf. A000045, A001175, A089911.
Sequence in context: A111301 A096320 A105955 * A152303 A064737 A098906
Adjacent sequences: A003890 A003891 A003892 * A003894 A003895 A003896
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KEYWORD
| nonn,base,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), ELIPPER(AT)UOFT02.UTOLEDO.EDU
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Nov 15 2003
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