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A302552 Number of segments needed to display the n-th prime number on a 7-segment LCD display. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

           _       _   _       _   _   _   _   _

          | |   |  _|  _| |_| |_  |_    | |_| |_|

          |_|   | |_   _|   |  _| |_|   | |_|  _|

.

The largest known Mersenne prime number, M(77232917), is a 23249425-digit number that would require 113927186 segments to display in its entirety. If each segment required 1 mW of electrical power, then to display the entire number for an hour would require about 114 KWh of energy!

LINKS

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

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", ")

        )

}

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

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Last modified August 20 05:25 EDT 2019. Contains 326139 sequences. (Running on oeis4.)