A166874 -id:A166874 - cp's OEIS frontend

A242590 Numbers whose representation in Roman numerals is horizontally symmetrical.

1, 2, 3, 9, 10, 11, 12, 13, 19, 20, 21, 22, 23, 29, 30, 31, 32, 33, 39, 90, 91, 92, 93, 99, 100, 101, 102, 103, 109, 110, 111, 112, 113, 119, 120, 121, 122, 123, 129, 130, 131, 132, 133, 139, 190, 191, 192, 193, 199, 200, 201, 202, 203, 209, 210, 211, 212, 213, 219, 220, 221, 222, 223, 229, 230, 231, 232, 233, 239, 290

Offset: 1

Philip Mizzi, May 24 2014

The sequence contains only 224 terms and ends with 899.

Roman numerals use the letters I, V, X, L, C, D and M, combinations of which are used to represent numbers. Since the letters V, L and M are not horizontally symmetrical, numbers containing these letters are not part of the sequence. Importantly, Roman numerals for 900 and beyond will always contain the numeral M, so the sequence ends at 899.

			Define two functions:
R(n) converts the number n to Roman number notation.
H[x] takes the argument x and produces a truth value, determining if the argument is horizontally symmetrical.
Hence,
for n = 1, R(n) = I, H[R(n)] = TRUE, so n = 1 is a term,
for n = 5, R(n) = V, H[R(n)] = FALSE, so n = 5 is not a term;
for n = 11, R(n) = XI, H[R(n)] = TRUE, so n = 11 is a term;
for n = 50, R(n) = L, H[R(n)] = FALSE, so n = 50 is not a term;
for n = 100, R(n) = C, H[R(n)] = TRUE, so n = 100 is a term;
for n = 900, R(n) = CM, H[R(n)] = FALSE, so n = 900 is not a term;
for n = 1000, R(n) = M, H[R(n)] = FALSE, so n = 1000 is not a term.

Philip Mizzi, Table of n, a(n) for n = 1..224

Cf. A007284 (horizontally/Arabic), A166874 (vertically/Roman).

Name edited by Jon E. Schoenfield, Sep 12 2017

A215121 Strobogrammatic palindromic numbers in their Roman numeral representation.

Original entry on oeis.org

1, 2, 3, 10, 19, 20, 30

Offset: 1

Jonathan Vos Post, Aug 03 2012

Numbers which, written as Roman numerals, are the same upside down and backwards.
Upside-down-invariant numbers are also called ambigrams. "Upside down" here means rotated by 180 degrees (i.e., central symmetry), NOT "vertically flipped" (symmetry w.r.t. horizontal line).
V, L, C, D, M (5, 50, 100, 500, 1000 in decimal) are not the same upside-down. Excludes "old style" Roman numeral representation of n (e.g., IIII rather than IV).

			I, II, III, X, XIX, XX, XXX.

Cf. A000787, A006968, A078715, A166874.

cp's OEIS Frontend

A242590 Numbers whose representation in Roman numerals is horizontally symmetrical.

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