A063720 Number of segments lit in a 7-segment display (as on a calculator) to represent the number n, variant 0: '6', '7' and '9' use 5, 3 and 5 segments, respectively.

6, 2, 5, 5, 4, 5, 5, 3, 7, 5, 8, 4, 7, 7, 6, 7, 7, 5, 9, 7, 11, 7, 10, 10, 9, 10, 10, 8, 12, 10, 11, 7, 10, 10, 9, 10, 10, 8, 12, 10, 10, 6, 9, 9, 8, 9, 9, 7, 11, 9, 11, 7, 10, 10, 9, 10, 10, 8, 12, 10, 11, 7, 10, 10, 9, 10, 10, 8, 12, 10, 9, 5, 8, 8, 7, 8, 8, 6, 10, 8, 13, 9, 12, 12, 11, 12

Offset: 0

Author

Deepan Majmudar (deepan.majmudar(AT)compaq.com), Aug 23 2001

Keywords

• nonn
• base
• nice

Comments

If we mark with * resp. ' the glyph variants (graphical representations) which use more resp. less segments, we have the following variants:

A063720 (this: 6', 7', 9'), A277116 (6*, 7', 9'), A074458 (6*, 7*, 9'), _________________________ A006942 (6*, 7', 9*), A010371 (6*, 7*, 9*). Sequences A234691, A234692 and variants make precise which segments are lit in each digit. These are related through the Hamming weight function A000120, e.g., A010371(n) = A000120(A234691(n)) = A000120(A234692(n)). - M. F. Hasler, Jun 17 2020

Examples

			The number 8 on a digital readout (e.g., on a calculator display) can be represented as
   -
  | |
   -
  | |
   -
which uses all 7 segments. Therefore a(8) = 7.
From _M. F. Hasler_, Jun 17 2020: (Start)
This sequence uses the following representations:
       _       _   _       _       _   _   _
      | |   |  _|  _| |_| |_  |_    | |_| |_|
      |_|   | |_   _|   |  _| |_|   | |_|   |
.
See crossrefs for other variants. (End)
		

Links

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

Crossrefs

For variants see A006942, A010371, A074458, A277116 (cf. comments).

Other related sequences: A018846, A018847, A018849, A038136, A053701.

Programs

Haskell

a063720 n = a063720_list !! n
a063720_list = [6,2,5,5,4,5,5,3,7,5] ++ f 10 where
   f x = (a063720 x' + a063720 d) : f (x + 1)
         where (x',d) = divMod x 10
-- Reinhard Zumkeller, Mar 15 2013

Mathematica

a[n_ /; n <= 9] := a[n] = {6, 2, 5, 5, 4, 5, 5, 3, 7, 5}[[n+1]]; a[n_] := a[n] = a[Quotient[n, 10]] + a[Mod[n, 10]]; Table[a[n], {n, 0, 85}] (* Jean-François Alcover, Aug 12 2013, after Reinhard Zumkeller *)
Table[Total[IntegerDigits[n]/.{0->6,1->2,2->5,3->5,6->5,7->3,8->7,9->5}],{n,0,90}] (* Harvey P. Dale, Mar 27 2021 *)

PARI

apply( {A063720(n)=digits(6255455375)[n%10+1]+if(n>9, self()(n\10))}, [0..99]) \\ M. F. Hasler, Jun 17 2020

Formula

a(n) = a(floor(n/10)) + a(n mod 10) for n > 9. - Reinhard Zumkeller, Mar 15 2013

a(n) <= A277116(n) <= min{A006942(n), A074458(n)} <= A010371(n); differences between these are given, e.g., by A102677(n) - A102679(n) (= number of digits 7 in n). - M. F. Hasler, Jun 17 2020

Extensions

More terms from Matthew Conroy, Sep 13 2001

Definition clarified by M. F. Hasler, Jun 17 2020