The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A278313 Number of letters "I" in Roman numeral representation of n. 1
 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0, 1, 2, 3, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Period 5: repeat [1, 2, 3, 1, 0]. - Omar E. Pol, Nov 19 2016 For large numbers we have the examples: 8000 -> VMMM (underline the V); 80000 -> LXXX (underline the LXXX); 800000 -> DCCC (underline the DCCC); ... see The Rules of Roman Numerals under Links. - José de Jesús Camacho Medina, Nov 21 2016 LINKS Table of n, a(n) for n=1..100. K6Math.com, The Rules of Roman Numerals Eric Weisstein's World of Mathematics, Roman numerals Wikipedia, Roman numerals Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,1). FORMULA a(n) = (n mod 5) - ((3n + 2n^2 + 3n^3 + 2n^4) mod 5). G.f.: x*(1 + 2*x + 3*x^2 + x^3)/((1 - x)*(1 + x + x^2 + x^3 + x^4)). - Ilya Gutkovskiy, Nov 20 2016 From Wesley Ivan Hurt, Dec 26 2016: (Start) a(n) = a(n-5) for n > 5. a(n) = (7 + (n mod 5) + 2*((n+1) mod 5) - ((n+2) mod 5) - ((n+3) mod 5) - ((n+4) mod 5))/5. (End) a(n) = 1 + (2/5)*(1 + 2*cos(2*(n-3)*Pi/5) + 2*cos(4*(n-3)*Pi/5) + cos(2*(n-2)*Pi/5) + cos(4*(n-2)*Pi/5) - cos(2*n*Pi/5) - cos(4*n*Pi/5)). - Wesley Ivan Hurt, Oct 04 2018 EXAMPLE a(1) = 1 because 1 in Roman numerals is I, which contains only one I. a(2) = 2 because 2 in Roman numerals is II, which contains two I's. a(3) = 3 because 3 in Roman numerals is III, which contains three I's. a(4) = 1 because 4 in Roman numerals is IV, which contains only one I. a(5) = 0 because 5 in Roman numerals is V, which does not contain I's. a(6) = 1 because 6 in Roman numerals is VI, which contains only one I. a(7) = 2 because 7 in Roman numerals is VII, which contains two I's. a(8) = 3 because 8 in Roman numerals is VIII, which contains three I's. a(9) = 1 because 9 in Roman numerals is IX, which contains only one I. a(10) = 0 because 10 in Roman numerals is X, which does not contain I's. a(50) = 0 because 50 in Roman numerals is L, which does not contain I's. a(100) = 0 because 100 in Roman numerals is C, which does not contain I's. a(500) = 0 because 500 in Roman numerals is D, which does not contain I's. a(551) = 1 because 551 in Roman numerals is DLI, which contains only one I. a(1000) = 0 because 1000 in Roman numerals is M, which does not contain I's. a(1001) = 1 because 1001 in Roman numerals is MI, which contains only one I. MAPLE A278313:= n -> [1, 2, 3, 1, 0][(n mod 5)+1]: seq(A278313(n), n=0..100); # Wesley Ivan Hurt, Dec 26 2016 MATHEMATICA Table[Mod[n, 5] - Mod[3n + 2n^2 + 3n^3 + 2n^4, 5], {n, 100}] Table[StringCount[RomanNumeral@ n, "I"], {n, 105}] (* Michael De Vlieger, Nov 24 2016, Version 10.2 *) PROG (Magma) &cat [[1, 2, 3, 1, 0]^^30]; // Wesley Ivan Hurt, Dec 26 2016 (PARI) Vec(x*(1 + 2*x + 3*x^2 + x^3)/((1 - x)*(1 + x + x^2 + x^3 + x^4)) + O(x^50)) \\ G. C. Greubel, Dec 26 2016 CROSSREFS Cf. A006968. Sequence in context: A321897 A050074 A346688 * A006705 A031269 A006703 Adjacent sequences: A278310 A278311 A278312 * A278314 A278315 A278316 KEYWORD nonn,base AUTHOR José de Jesús Camacho Medina, Nov 17 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 11 09:25 EDT 2024. Contains 375815 sequences. (Running on oeis4.)