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Number of dots needed to express n as a Roman numeral in Braille.
0

%I #10 Mar 08 2014 08:35:32

%S 2,4,6,6,4,6,8,10,6,4,6,8,10,10,8,10,12,14,10,8,10,12,14,14,12,14,16,

%T 18,14,12,14,16,18,18,16,18,20,22,18,7,9,11,13,13,11,13,15,17,13,3,5,

%U 7,9,9,7,9,11,13,9,7,9,11,13,13,11,13,15,17,13,11,13,15

%N Number of dots needed to express n as a Roman numeral in Braille.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Braille">Braille</a>

%e VII in Braille (with the "Roman num" character):

%e o o o o

%e o o o

%e o o o

%e Therefore a(7) = 10 - 2 = 8.

%o (PARI) a=[2, 4, 6, 6, 4, 6, 8, 10, 6, 0]; b=[0, 4, 8, 12, 7, 3, 7, 11, 15, 6]; for(n=1, 72, if(n<100, print1(a[lift(Mod(n-1, 10))+1]+b[floor(n/10)+1], ", "), break));

%o (PARI)

%o /* The program works for n < 40 */

%o b=0; for(n=1, 39, if(Mod(n, 10)==0, b=b+4); m=lift(Mod(n, 10)); a=2*m-6; if(Mod(m, 5)==4, d=abs(a-7)+b+1, if(m<4, d=a+b+6, d=a+b)); print1(d, ", "));

%Y Cf. also A002963, A048181, A030166, A072283, A079399, A121018, A220090.

%K nonn,word,base

%O 1,1

%A _Arkadiusz Wesolowski_, Feb 25 2014