A285511 Value of the n-th Roman number interpreted as Latin alphabetic number.

9, 243, 6327, 256, 22, 581, 15115, 392999, 258, 24, 633, 16467, 428151, 16480, 646, 16805, 436939, 11360423, 16482, 648, 16857, 438291, 11395575, 438304, 16870, 438629, 11404363, 296513447, 438306, 16872, 438681, 11405715, 296548599, 11405728, 438694, 11406053, 296557387, 7710492071, 11405730, 636

Offset: 1

Author

Martin Janecke, Apr 20 2017

Keywords

• nonn
• base
• easy
• fini
• full

Comments

Lists can be numbered using different counter styles, for example using the Latin alphabet A, B, C, ..., Z, AA, AB, ... or the Roman number system I, II, III, IV, V, VI, ... Both these counter styles are defined in CSS Counter Styles Level 3 as "upper-alpha" and "upper-roman". Roman number representations are defined for the range 1 to 3999 only. Roman numerals are a subset of Latin alphabet letters; for every Roman number there is exactly one alphabetic number that looks identical. Denote the n-th Roman number by R(n) and the m-th alphabetic number by L(m), then R(n) and L(a(n)) look identical.

Examples

			The number n = 1 is written "I" in the Roman number system. "I" being the ninth letter in the alphabet is also the ninth number in the alphabetic number system. Therefore a(1) = 9.
The number n = 2 is written "II" in the Roman number system. "II" is also the 243rd number in the alphabetic number system, because "I" is the ninth letter in the 26-letter alphabet and 9*26^1+9*26^0 = 243. Therefore a(2) = 243.
The number n = 3 is written "III" in the Roman number system. "III" is also the 6327th number in the alphabetic number system because "I" is the ninth letter in the 26-letter alphabet and 9*26^2+9*26^1+9*26^0 = 6327. Therefore a(3) = 6327.
The number n = 4 is written "IV" in the Roman number system. "IV" is also the 256th number in the alphabetic number system because "I" is the ninth letter in the 26-letter alphabet and "V" is the 22nd letter, therefore a(4) = 9*26^1 + 22 = 256.
The number n = 600 is written "DC" in the Roman number system. "DC" is also the 107th number in the alphabetic number system, because "D" and "C" are the fourth and third letters in the 26-letter alphabet and 4*26^1+3*26^0 = 107. Therefore a(600) = 107.
		

Links

• Martin Janecke, Table of n, a(n) for n = 1..3999
• Tab Atkins Jr. et al., CSS Counter Styles Level 3 (W3C Candidate Recommendation), 11 June 2015
• Martin Janecke, Roman numbers ↔ Latin alphabet counter, April 2017

Crossrefs

Cf. A006968, A009970, A061493.