A302552 - OEIS

%I #37 Oct 30 2020 15:39:08

%S 5,5,5,3,4,7,5,8,10,11,7,8,6,9,7,10,11,8,9,5,8,9,12,13,9,10,13,11,14,

%T 9,10,9,10,13,12,9,10,13,11,10,11,11,10,13,11,14,9,15,13,16,15,16,11,

%U 12,13,16,17,10,11,14,17,16,14,9,12,10,12,13,12,15,15

%N Number of segments needed to display the n-th prime number on a 7-segment LCD display.

%C            _       _   _       _   _   _   _   _

%C           | |   |  _|  _| |_| |_  |_    | |_| |_|

%C           |_|   | |_   _|   |  _| |_|   | |_|  _|

%C .

%H <a href="/index/Ca#calculatordisplay">Index entries for sequences related to calculator display</a>

%F a(n) = A006942(A000040(n)). - _Alois P. Heinz_, Jun 20 2018

%e For n = 6, prime(6) = 13, which has two digits: 1, 3. We need two segments for the 1 and five for the 3 (see the Comments section), so a(6) = 2 + 5 = 7.

%p a:= n-> add([6,2,5,5,4,5,6,3,7,6][i+1], i=convert(ithprime(n), base, 10)):

%p seq(a(n), n=1..100);  # _Alois P. Heinz_, Jun 20 2018

%t f[n_] := Plus @@ (IntegerDigits@n /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 7 -> 3, 8 -> 7, 9 -> 6}); f@# & /@ Prime@ Range@ 71 (* _Robert G. Wilson v_, Jun 20 2018 *)

%o (PARI) {

%o v=vector(10);

%o v[1]=6;v[2]=2;v[3]=5;v[4]=5;v[5]=4;v[6]=5;v[7]=6;v[8]=3;v[9]=7;v[10]=6;

%o forprime(n=2,1000,

%o          d=digits(n,10);s=0;

%o          for(i=1,#d,

%o              s+=v[d[i]+1];

%o             )

%o         ;print1(s", ")

%o         )

%o }

%o (Python)

%o from sympy import prime

%o def A302552(n):

%o     return sum((6, 2, 5, 5, 4, 5, 6, 3, 7, 6)[int(d)] for d in str(prime(n))) # _Chai Wah Wu_, Oct 30 2020

%Y Cf. A000040, A006942.

%K nonn,easy,base

%O 1,1

%A _Dimitris Valianatos_, Jun 20 2018