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A078715 Palindromic Roman numerals.

%I A078715 #29 Feb 16 2025 08:32:48
%S A078715 1,2,3,5,10,19,20,30,50,100,190,200,300,500,1000,1900,2000,3000
%N A078715 Palindromic Roman numerals.
%C A078715 This sequence is consistent with the Roman numerals as expressed in the Schildberger link. 4 (usually IV now) could be included in a variant of this sequence as IIII is sometimes used (especially on clock faces). To make this or similar sequences well-defined for numbers larger than 3999, it must be decided whether and how to handle the apostrophus (backward-C), the vinculum (bar), the frame, or even other multiplier notations used at various times in representations of larger Roman numerals. Recalling the "Y2K crisis", will there be a(n even milder) "Y4M crisis"? In particular, is 4000 to be represented as MMMM, (I)(I)(I)(I) (where parentheses are used to represent C and the apostrophus), MV (with vinculum over the V), IV (with vinculum over both I and V) or IIII with vinculum over all four I's? If there is no general agreement, could Roman civilization be at risk (once again)?
%C A078715 Indices of terms in A061493 which are also in A002113. - _M. F. Hasler_, Jan 12 2015
%D A078715 Encyclopaedia Britannica, 1981 ed., Vol. 11, "Mathematics, History of", p. 647.
%D A078715 Webster's Third New International Dictionary (Unabridged), 1976 ed., "Cardinal Numbers Table" and footnotes, p. 1549.
%H A078715 Paul Lewis, <a href="http://www.web40571.clarahost.co.uk/roman/front.htm">Roman numerals and calendar</a>
%H A078715 Gerard Schildberger, <a href="/A006968/a006968.txt">The first 3999 numbers in Roman numerals</a>
%H A078715 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RomanNumerals.html">Roman Numerals</a>
%F A078715 A136522(A061493(a(n))) = 1. - _Reinhard Zumkeller_, Apr 14 2013
%e A078715 I, II, III, V, X, XIX, XX, XXX, L, C, CXC, CC, CCC, D, M, MCM, MM, MMM
%t A078715 Select[Range[3000], PalindromeQ[RomanNumeral[#]] &] (* _Paolo Xausa_, Mar 03 2024 *)
%o A078715 (Haskell)
%o A078715 a078715 n = a078715_list !! (n-1)
%o A078715 a078715_list = filter ((== 1) . a136522 . a061493) [1..3999]
%o A078715 -- _Reinhard Zumkeller_, Apr 14 2013
%o A078715 (PARI) is_A078715(n)=Vecrev(n=Str(A061493(n)))==Vec(n) \\ _M. F. Hasler_, Jan 12 2015
%Y A078715 Cf. A061493, A006968 (Roman numerals main entry), A002113 (Palindromic Arabic numerals).
%Y A078715 Subsequence of A093703.
%K A078715 base,easy,nonn,fini,full
%O A078715 1,2
%A A078715 _Rick L. Shepherd_, Dec 19 2002