A277116 Number of segments used to represent the number n on a 7-segment display: variant where digits 6, 7 and 9 use 6, 3 and 5 segments, respectively.

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

Offset: 0

Author

Eric Ginsburg, Sep 30 2016

Keywords

• nonn
• easy
• base

Comments

Another version of A006942. Here the digit "6" is represented with six segments (the same as in A006942) but the digit "9" is represented with five segments instead of six segments. - Omar E. Pol, Sep 30 2016

If we mark with * resp. ' the graphical representations which use one more resp. one less segment, 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*).

Sequences A234691 and A234692 make precise which segments are lit in each digit. They 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

			For n = 29, digit '2' uses 5 segments and digit '9' uses 5 segments. So, a(29) = 10. - _Indranil Ghosh_, Feb 02 2017
The digits are represented as follows:
   _     _  _       _   _   _   _   _
  | | |  _| _| |_| |_  |_    | |_| |_|
  |_| | |_  _|   |  _| |_|   | |_|   | . - _M. F. Hasler_, Jun 17 2020
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..50000
• Wikipedia, Seven-segment display.
• Index entries for sequences related to calculator display

Crossrefs

Segment variations: A006942, A010371, A063720, A074458.

Cf. A102683, A234691, A234692.

Programs

Mathematica

Table[Total[IntegerDigits[n] /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 6 -> 6, 7 -> 3, 8 -> 7, 9 -> 5}], {n, 0, 120}] (* Michael De Vlieger, Sep 30 2016 *)

PARI

a(n) = my(segm=[6, 2, 5, 5, 4, 5, 6, 3, 7, 5], d=digits(n), s=0); if(n==0, s=6, for(k=1, #d, s=s+segm[d[k]+1])); s \\ Felix Fröhlich, Oct 05 2016

Python

def A277116(n):
    s=0
    for i in str(n):
        s+=[6,2,5,5,4,5,6,3,7,5][int(i)]
    return s # Indranil Ghosh, Feb 02 2017

Formula

a(n) = A006942(n) - A102683(n). - Omar E. Pol, Sep 30 2016

a(n) = A063720(n) + A102677(n) - A102679(n) (add number of digits 6)

= A074458(n) - A102679(n) + A102681(n) (subtract number of digits 7)

and thus A063720(n) <= a(n) <= min(A074458(n), A006942(n)) <= A010371(n). - M. F. Hasler, Jun 17 2020

Extensions

Better definition and more terms from Omar E. Pol, Sep 30 2016

Edited by M. F. Hasler, Jun 17 2020