%I #54 Sep 01 2020 06:24:56
%S 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,
%T 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,
%U 8,12,10,12,8,11,11,10,11,12,9,13,11,9,5,8,8,7,8,9
%N 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.
%C 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
%C If we mark with * resp. ' the graphical representations which use one more resp. one less segment, we have the following variants:
%C A063720 (6', 7', 9'), A277116 (6*, 7', 9'), A074458 (6*, 7*, 9'),
%C _____________________ A006942 (6*, 7', 9*), A010371 (6*, 7*, 9*).
%C 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
%H Indranil Ghosh, <a href="/A277116/b277116.txt">Table of n, a(n) for n = 0..50000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Seven-segment_display">Seven-segment display</a>.
%H <a href="/index/Ca#calculatordisplay">Index entries for sequences related to calculator display</a>
%F a(n) = A006942(n) - A102683(n). - _Omar E. Pol_, Sep 30 2016
%F a(n) = A063720(n) + A102677(n) - A102679(n) (add number of digits 6)
%F = A074458(n) - A102679(n) + A102681(n) (subtract number of digits 7)
%F and thus A063720(n) <= a(n) <= min(A074458(n), A006942(n)) <= A010371(n). - _M. F. Hasler_, Jun 17 2020
%e For n = 29, digit '2' uses 5 segments and digit '9' uses 5 segments. So, a(29) = 10. - _Indranil Ghosh_, Feb 02 2017
%e The digits are represented as follows:
%e _ _ _ _ _ _ _ _
%e | | | _| _| |_| |_ |_ | |_| |_|
%e |_| | |_ _| | _| |_| | |_| | . - _M. F. Hasler_, Jun 17 2020
%t 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 *)
%o (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
%o (Python)
%o def A277116(n):
%o s=0
%o for i in str(n):
%o s+=[6,2,5,5,4,5,6,3,7,5][int(i)]
%o return s # _Indranil Ghosh_, Feb 02 2017
%Y Segment variations: A006942, A010371, A063720, A074458.
%Y Cf. A102683, A234691, A234692.
%K nonn,easy,base
%O 0,1
%A _Eric Ginsburg_, Sep 30 2016
%E Better definition and more terms from _Omar E. Pol_, Sep 30 2016
%E Edited by _M. F. Hasler_, Jun 17 2020