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%I #33 Mar 27 2021 13:24:30
%S 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,
%T 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,
%U 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
%N 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.
%C If we mark with * resp. ' the glyph variants (graphical representations) which use more resp. less segments, we have the following variants:
%C 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
%H Reinhard Zumkeller, <a href="/A063720/b063720.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Ca#calculatordisplay">Index entries for sequences related to calculator display</a>
%F a(n) = a(floor(n/10)) + a(n mod 10) for n > 9. - _Reinhard Zumkeller_, Mar 15 2013
%F 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
%e The number 8 on a digital readout (e.g., on a calculator display) can be represented as
%e -
%e | |
%e -
%e | |
%e -
%e which uses all 7 segments. Therefore a(8) = 7.
%e From _M. F. Hasler_, Jun 17 2020: (Start)
%e This sequence uses the following representations:
%e _ _ _ _ _ _ _
%e | | | _| _| |_| |_ |_ | |_| |_|
%e |_| | |_ _| | _| |_| | |_| |
%e .
%e See crossrefs for other variants. (End)
%t 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_ *)
%t 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 *)
%o (Haskell)
%o a063720 n = a063720_list !! n
%o a063720_list = [6,2,5,5,4,5,5,3,7,5] ++ f 10 where
%o f x = (a063720 x' + a063720 d) : f (x + 1)
%o where (x',d) = divMod x 10
%o -- _Reinhard Zumkeller_, Mar 15 2013
%o (PARI) apply( {A063720(n)=digits(6255455375)[n%10+1]+if(n>9, self()(n\10))}, [0..99]) \\ _M. F. Hasler_, Jun 17 2020
%Y For variants see A006942, A010371, A074458, A277116 (cf. comments).
%Y Other related sequences: A018846, A018847, A018849, A038136, A053701.
%K nonn,base,nice
%O 0,1
%A Deepan Majmudar (deepan.majmudar(AT)compaq.com), Aug 23 2001
%E More terms from _Matthew Conroy_, Sep 13 2001
%E Definition clarified by _M. F. Hasler_, Jun 17 2020
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