A036746 Numbers with "long" representations in Roman notation: given by last n letters from ...MMMDCCCLXXXVIII.

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

Offset: 1

Author

J. H. Conway

Keywords

• nonn
• base
• easy

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).

Crossrefs

Cf. A061493, A006968, A003587.

Programs

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

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 *)

PARI

A036746(n)=(n%4+8/9)\.1^(n\4) \\ M. F. Hasler, Jan 12 2015

Formula

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

Extensions

Checked by Robert G. Wilson v, Aug 13 2008

Edited by M. F. Hasler, Jan 12 2015