A036746 - OEIS

%I #17 Apr 14 2022 16:09:16

%S 1,2,3,8,18,28,38,88,188,288,388,888,1888,2888,3888

%N Numbers with "long" representations in Roman notation: given by last n letters from ...MMMDCCCLXXXVIII.

%C 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

%H Matt Parker, <a href="https://www.youtube.com/watch?v=jMxoGqsmk5Y">How Roman numerals broke the official dog database</a>, YouTube video (2022).

%H Gerard Schildberger, <a href="/A006968/a006968.txt"> The first 3999 numbers in Roman numerals</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = min{ k>0 | A006968(k)=n }. - _M. F. Hasler_, Jan 12 2015

%t (* 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 *)

%o (Haskell)

%o import Data.List (inits, elemIndex)

%o import Data.Maybe (mapMaybe)

%o a036746 n = a036746_list !! (n-1)

%o a036746_list = map (+ 1) $ mapMaybe (`elemIndex` a061493_list)

%o    (map (read . reverse) $ tail $ inits $ reverse $ show $ a061493 3888)

%o -- _Reinhard Zumkeller_, Apr 14 2013

%o (PARI) A036746(n)=(n%4+8/9)\.1^(n\4) \\ _M. F. Hasler_, Jan 12 2015

%Y Cf. A061493, A006968, A003587.

%K nonn,base,easy

%O 1,2

%A _J. H. Conway_

%E Checked by _Robert G. Wilson v_, Aug 13 2008

%E Edited by _M. F. Hasler_, Jan 12 2015