A302552 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

_ _ _ _ _ _ _ _

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

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

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", ")

)

}