%I #47 Sep 01 2020 06:24:48

%S 6,2,5,5,4,5,6,4,7,6,8,4,7,7,6,7,8,6,9,8,11,7,10,10,9,10,11,9,12,11,

%T 11,7,10,10,9,10,11,9,12,11,10,6,9,9,8,9,10,8,11,10,11,7,10,10,9,10,

%U 11,9,12,11,12,8,11,11,10,11,12,10,13,12,10,6,9,9,8,9,10,8,11,10,13,9,12,12

%N Number of segments used to represent n on a 7-segment calculator display; version where '6', '7' and '9' use 6, 4 and 6 segments, respectively.

%C Except for 1 and 3 every positive integer occurs; A143616 and A143617 give record values and where they occur. - _Reinhard Zumkeller_, Aug 27 2008

%C The difference between this sequence and A006942 lies in the representation chosen for the digit 7,

%C _ _

%C | | |

%C | (here), vs. | in A006942.

%C If we mark with ' the "sans serif" graphical representation which uses one segment less and with * the "heavier" version, 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*) = this.

%C Sequences A234691, A234692 and variants make precise which segments are lit in each digit. They are related through the Hamming weight A000120, see formula. The sequence could be extended to negative arguments with a(-n) = a(n)+1. - _M. F. Hasler_, Jun 17 2020

%H R. Zumkeller, <a href="/A010371/b010371.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 For n > 9, a(n) = a(floor(n/10)) + a(n mod 10). - _Reinhard Zumkeller_, Aug 27 2008

%F a(n) = A000120(A234691(n)) = A000120(A234692(n))

%F = A006942(n) + A102679(n) - A102681(n) (add number of digits 7)

%F = A074458(n) + A102683(n) (add number of digits 9). - _M. F. Hasler_, Jun 17 2020

%e LCD Display (cf. Casio scientific calculator fx-3600P):

%e _ _ _ _ _ _ _ _

%e | | | _| _| |_| |_ |_ | | |_| |_|

%e |_| | |_ _| | _| |_| | |_| _|

%t MapIndexed[(f[#2[[1]]-1] = #1)&, {6, 2, 5, 5, 4, 5, 6, 4, 7, 6}]; a[n_] := Total[f /@ IntegerDigits[n]]; Table[a[n], {n, 0, 100}] (* _Jean-François Alcover_, Mar 08 2017 *)

%o (Haskell)

%o a010371 n = a010371_list !! n

%o a010371_list = [6,2,5,5,4,5,6,4,7,6] ++ f 10 where

%o f x = (a010371 x' + a010371 d) : f (x + 1)

%o where (x',d) = divMod x 10

%o -- _Reinhard Zumkeller_, Mar 15 2013

%o (PARI) apply( {A010371(n)=digits(6255456476)[n%10+1]+if(n>9, self()(n\10))}, [0..99]) \\ M. F. Hasler, Jun 17 2020

%Y Segment variations: A006942, A063720, A074458, A277116.

%Y Cf. A000120, A234691, A234692.

%K nonn,base,easy,nice,look

%O 0,1

%A Olivier.Gagneux(AT)roche.com

%E Corrected and extended by Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 27 1999

%E Edited name, comments, cross-references. - _M. F. Hasler_, Jun 17 2020