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

0,1

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

Links

Indranil Ghosh, Table of n, a(n) for n = 0..50000

Wikipedia, Seven-segment display.

Index entries for sequences related to calculator display

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

Example

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

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 *)

Prog

(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

Crossrefs

Segment variations: A006942, A010371, A063720, A074458.

Cf. A102683, A234691, A234692.

Sequence in context: A258102 A309449 A063720 * A006942 A074458 A010371

Adjacent sequences: A277113 A277114 A277115 * A277117 A277118 A277119

Keyword

nonn,easy,base

Author

Eric Ginsburg, Sep 30 2016

Extensions

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

Edited by M. F. Hasler, Jun 17 2020

Status

approved