OFFSET
1,2
COMMENTS
Also: Least number using n symbols when written as Roman numeral, cf. A006968 and A061493. One could prefix a conventional a(0)=0. - M. F. Hasler, Jan 12 2015
LINKS
Matt Parker, How Roman numerals broke the official dog database, YouTube video (2022).
Gerard Schildberger, The first 3999 numbers in Roman numerals.
Index entries for linear recurrences with constant coefficients, signature (2,-1).
FORMULA
a(n) = min{ k>0 | A006968(k)=n }. - M. F. Hasler, Jan 12 2015
MATHEMATICA
(* assign the 3999 Roman numerals to the variable 'lst' so that lst = {I, II, III, ... MMMCMXCVII, MMMCMXCVIII, MMMCMXCIX}, e.g. using the link to Schildberger's file, then *) f[1] = 1; f[n_] := Block[{k = 2}, While[ StringLength@ SymbolName@ lst[[k]] != n, k++ ]; k]; Array[f, 15] (* Checked by Robert G. Wilson v, Aug 13 2008; edited by M. F. Hasler, Jan 12 2015 *)
PROG
(Haskell)
import Data.List (inits, elemIndex)
import Data.Maybe (mapMaybe)
a036746 n = a036746_list !! (n-1)
a036746_list = map (+ 1) $ mapMaybe (`elemIndex` a061493_list)
(map (read . reverse) $ tail $ inits $ reverse $ show $ a061493 3888)
-- Reinhard Zumkeller, Apr 14 2013
(PARI) A036746(n)=(n%4+8/9)\.1^(n\4) \\ M. F. Hasler, Jan 12 2015
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
EXTENSIONS
Checked by Robert G. Wilson v, Aug 13 2008
Edited by M. F. Hasler, Jan 12 2015
STATUS
approved