A302552 Number of segments needed to display the n-th prime number on a 7-segment LCD display.

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

Offset: 1

Author

Dimitris Valianatos, Jun 20 2018

Keywords

• nonn
• easy
• base

Comments

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Examples

			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.
		

Links

• Index entries for sequences related to calculator display

Crossrefs

Cf. A000040, A006942.

Programs

Maple

a:= n-> add([6,2,5,5,4,5,6,3,7,6][i+1], i=convert(ithprime(n), base, 10)):
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 20 2018

Mathematica

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 *)

PARI

{
v=vector(10);
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;
forprime(n=2,1000,
         d=digits(n,10);s=0;
         for(i=1,#d,
             s+=v[d[i]+1];
            )
        ;print1(s", ")
        )
}

Python

from sympy import prime
def A302552(n):
    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

Formula

a(n) = A006942(A000040(n)). - Alois P. Heinz, Jun 20 2018