A180105 Counting integers normally (1, 2, 3, 4, 5...), write them as roman numerals (I, II, III, IV, V...), describe them (one 1, two 1s, three 1s, one 1 one 5, one 5...), and write them out as numbers (11, 21, 31, 1115, 15...).

11, 21, 31, 1115, 15, 1511, 1521, 1531, 11110, 110, 11011, 11021, 11031, 1101115, 11015, 1101511, 1101521, 1101531, 11011110, 210, 21011, 21021, 21031, 2101115, 21015, 2101511, 2101521, 2101531, 21011110, 310, 31011, 31021, 31031, 3101115, 31015, 3101511

Offset

1,1

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..3999

David Consiglio, Jr., Python program

Example

For n=9, IX gives one 1 and one 10, so a(9) = 11110.

Mathematica

f[n_] := Block[{w = RomanNumeral@ n}, FromDigits@ Flatten[IntegerDigits /@ {Length@ #, FromRomanNumeral@ First@ #} & /@ Split@ StringPartition[w, 1]]]; Array[f, {36}] (* Michael De Vlieger, Oct 13 2015, Version 10.2 *)

Crossrefs

Sequence in context: A181178 A178205 A239464 * A288186 A264646 A139113

Adjacent sequences: A180102 A180103 A180104 * A180106 A180107 A180108

Keyword

nonn,base

Author

Saiichi Shayan Hashimoto (drako3759(AT)gmail.com), Aug 09 2010

Extensions

a(9) and a(19) corrected by David Consiglio, Jr., Oct 12 2015

More terms from David Consiglio, Jr., Oct 12 2015

Status

approved