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A222581 Run lengths of digits when concatenating Roman numerals less than 4000, cf. A093796. 2
7, 3, 1, 1, 2, 1, 4, 3, 1, 1, 2, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 5, 1, 2, 2, 2, 3, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 1, 7, 1, 3, 2, 3, 3, 3, 1, 1, 3, 1, 3, 1, 1, 3, 1, 2, 3, 1, 3, 3, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

See A078715 for a discussion on the Roman 4M-problem;

a(n) <= 7, that is, the longest run of consecutive equal digits in A093796 has length = 7; see also example.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..19770

Eric Weisstein's World of Mathematics, Roman Numerals

Wikipedia, Roman numerals

EXAMPLE

The 3999 Roman numerals of all numbers less than 4000 consist of 30000 digits; there are 19777 runs of consecutive equal digits: a(19777) = 1 is the last term of this sequence;

a(1)=a(52)=7, there are two runs with length 7: the first is "IIIIIII" which is the prefix of the concatenation of I, II, III and IV, the second is "XXXXXXX" which is contained in the concatenation of XXIX, XXX and XXXI;

a(1022)=a(14573)=6, there are also two runs with length 6: the first is "CCCCCC" which is a prefix of the concatenation of CCC and CCCI, the second is "MMMMMM" which is a prefix of the concatenation of MMM and MMMI;

a(30)=5, there is just one run with length 5: "XXXXX" which is contained in the concatenation of XIX, XX and XXI;

a(7)=a(644)=a(1359)=a(9375)=a(19194)=4, there are five runs with length 4: "IIII", two times "CCCC" and "MMMM", they occur in concatenations of (VIII, IX), (CC, CCI), (CCCXC, CCCXCI), (MM, MMI), (MMMCM, MMMCMI), respectively.

PROG

(Haskell)

import Data.List (group)

a222581 n = a222581_list !! (n-1)

a222581_list = map length $ group a093796_list

CROSSREFS

Sequence in context: A083803 A136595 A111475 * A010139 A078075 A067616

Adjacent sequences:  A222578 A222579 A222580 * A222582 A222583 A222584

KEYWORD

nonn,base,fini,full

AUTHOR

Reinhard Zumkeller, Apr 14 2013

STATUS

approved

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Last modified May 17 19:39 EDT 2021. Contains 343988 sequences. (Running on oeis4.)