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

1,1

Comments

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Links

Table of n, a(n) for n=1..71.

Index entries for sequences related to calculator display

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000040, A006942.

Sequence in context: A094851 A173602 A054245 * A193887 A196998 A232614

Adjacent sequences: A302549 A302550 A302551 * A302553 A302554 A302555

Keyword

nonn,easy,base

Author

Dimitris Valianatos, Jun 20 2018

Status

approved