A010371 - OEIS

A010371

Number of segments used to represent n on a 7-segment calculator display; version where '6', '7' and '9' use 6, 4 and 6 segments, respectively.

6, 2, 5, 5, 4, 5, 6, 4, 7, 6, 8, 4, 7, 7, 6, 7, 8, 6, 9, 8, 11, 7, 10, 10, 9, 10, 11, 9, 12, 11, 11, 7, 10, 10, 9, 10, 11, 9, 12, 11, 10, 6, 9, 9, 8, 9, 10, 8, 11, 10, 11, 7, 10, 10, 9, 10, 11, 9, 12, 11, 12, 8, 11, 11, 10, 11, 12, 10, 13, 12, 10, 6, 9, 9, 8, 9, 10, 8, 11, 10, 13, 9, 12, 12

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

OFFSET

0,1

COMMENTS

Except for 1 and 3 every positive integer occurs; A143616 and A143617 give record values and where they occur. - Reinhard Zumkeller, Aug 27 2008

The difference between this sequence and A006942 lies in the representation chosen for the digit 7,

_ _

| | |

| (here), vs. | in A006942.

If we mark with ' the "sans serif" graphical representation which uses one segment less and with * the "heavier" version, we have the following variants:

A063720 (6', 7', 9'), A277116 (6*, 7', 9'), A074458 (6*, 7*, 9'),

_____________________ A006942 (6*, 7', 9*), A010371 (6*, 7*, 9*) = this.

Sequences A234691, A234692 and variants make precise which segments are lit in each digit. They are related through the Hamming weight A000120, see formula. The sequence could be extended to negative arguments with a(-n) = a(n)+1. - M. F. Hasler, Jun 17 2020

LINKS

R. Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to calculator display

FORMULA

For n > 9, a(n) = a(floor(n/10)) + a(n mod 10). - Reinhard Zumkeller, Aug 27 2008

a(n) = A000120(A234691(n)) = A000120(A234692(n))

= A006942(n) + A102679(n) - A102681(n) (add number of digits 7)

= A074458(n) + A102683(n) (add number of digits 9). - M. F. Hasler, Jun 17 2020

EXAMPLE

LCD Display (cf. Casio scientific calculator fx-3600P):

_ _ _ _ _ _ _ _

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

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

MATHEMATICA

MapIndexed[(f[#2[[1]]-1] = #1)&, {6, 2, 5, 5, 4, 5, 6, 4, 7, 6}]; a[n_] := Total[f /@ IntegerDigits[n]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Mar 08 2017 *)

PROG

(Haskell)

a010371 n = a010371_list !! n

a010371_list = [6, 2, 5, 5, 4, 5, 6, 4, 7, 6] ++ f 10 where

f x = (a010371 x' + a010371 d) : f (x + 1)

where (x', d) = divMod x 10

-- Reinhard Zumkeller, Mar 15 2013

(PARI) apply( {A010371(n)=digits(6255456476)[n%10+1]+if(n>9, self()(n\10))}, [0..99]) \\ M. F. Hasler, Jun 17 2020

CROSSREFS

Segment variations: A006942, A063720, A074458, A277116.

Cf. A000120, A234691, A234692.

Sequence in context: A277116 A006942 A074458 * A270614 A011489 A093601