A078715 Palindromic Roman numerals.

1, 2, 3, 5, 10, 19, 20, 30, 50, 100, 190, 200, 300, 500, 1000, 1900, 2000, 3000

Offset: 1

Author

Rick L. Shepherd, Dec 19 2002

Keywords

• base
• easy
• nonn
• fini
• full

Comments

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)?

Indices of terms in A061493 which are also in A002113. - M. F. Hasler, Jan 12 2015

Examples

			I, II, III, V, X, XIX, XX, XXX, L, C, CXC, CC, CCC, D, M, MCM, MM, MMM
		

References

• Encyclopaedia Britannica, 1981 ed., Vol. 11, "Mathematics, History of", p. 647.
• Webster's Third New International Dictionary (Unabridged), 1976 ed., "Cardinal Numbers Table" and footnotes, p. 1549.

Links

• Paul Lewis, Roman numerals and calendar
• Gerard Schildberger, The first 3999 numbers in Roman numerals
• Eric Weisstein's World of Mathematics, Roman Numerals

Crossrefs

Cf. A061493, A006968 (Roman numerals main entry), A002113 (Palindromic Arabic numerals).

Subsequence of A093703.

Programs

Haskell

a078715 n = a078715_list !! (n-1)
a078715_list = filter ((== 1) . a136522 . a061493) [1..3999]
-- Reinhard Zumkeller, Apr 14 2013

Mathematica

Select[Range[3000], PalindromeQ[RomanNumeral[#]] &] (* Paolo Xausa, Mar 03 2024 *)

PARI

is_A078715(n)=Vecrev(n=Str(A061493(n)))==Vec(n) \\ M. F. Hasler, Jan 12 2015

Formula

A136522(A061493(a(n))) = 1. - Reinhard Zumkeller, Apr 14 2013