A160754 Numbers k such that k, 2k, 3k and 4k use the same number of characters when expressed in Roman numerals.

36, 153, 315, 351, 360, 448, 736, 1386

Offset: 1

Author

Claudio Meller, May 25 2009

Keywords

• nonn
• easy

Comments

This sequence is complete up to 3999.

Examples

			1*36 =  36 = XXXVI,
2*36 =  72 = LXXII,
3*36 = 108 = CVIII,
4*36 = 144 = CXLIV,
so 36 is a term;
1*153 = 153 = CLIII,
2*153 = 306 = CCCVI,
3*153 = 459 = CDLIX,
4*153 = 612 = DCXII,
so 153 is a term.
		

Crossrefs

See A006968 for the basic underlying sequence.

Programs

Maple

for n from 1 to 3999 do if(length(convert(n, roman)) = length(convert(2*n, roman)) and length(convert(n, roman)) = length(convert(3*n, roman)) and length(convert(n, roman)) = length(convert(4*n, roman)))then printf("%d, ", n): fi: od: # Nathaniel Johnston, May 18 2011

Extensions

a(8) from Nathaniel Johnston, May 18 2011