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

1,1

Comments

This sequence is complete up to 3999.

Links

Table of n, a(n) for n=1..8.

Example

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.

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

Crossrefs

See A006968 for the basic underlying sequence.

Sequence in context: A039495 A263120 A034592 * A275496 A117511 A250632

Adjacent sequences: A160751 A160752 A160753 * A160755 A160756 A160757

Keyword

nonn,easy

Author

Claudio Meller, May 25 2009

Extensions

a(8) from Nathaniel Johnston, May 18 2011

Status

approved