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

Offset: 0

Author

Olivier.Gagneux(AT)roche.com

Keywords

• nonn
• base
• easy
• nice
• look

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

Examples

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

Links

• R. Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to calculator display

Crossrefs

Segment variations: A006942, A063720, A074458, A277116.

Cf. A000120, A234691, A234692.

Programs

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

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 *)

PARI

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

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

Extensions

Corrected and extended by Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 27 1999

Edited name, comments, cross-references. - M. F. Hasler, Jun 17 2020