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%I #33 Jan 27 2024 18:41:19
%S 1,2,6,8,10,18,20,28,68,88,108,188,200,208,288,688,888,1088,1888,2008,
%T 2088,2888,6888,8888,10888,18888,20088,20888,28888,68888,88888,108888,
%U 188888,200888,208888,288888,688888,888888,1088888,1888888,2008888,2088888,2888888,6888888,8888888
%N Smallest positive number that needs more lines when shown on a 7-segment display (digital clock) than any previous term.
%C For n > 1, a(n) uses n + 3 segments to be displayed, when a digit '6' uses 6 segments (as in A234691, A234692 and A277116, A074458, A006942, A010371, but not in A063720). Sequence A143617 is the same but starts with 0, 8, ... and A216261 has additional terms 7 & 4 before 2 and 22 before 20. - _M. F. Hasler_, Jun 23 2020
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,10,-10).
%F For n >= 3, the terms with n digits are given by: 108*A + B, 188*A + B, 200*A + B, 208*A + B, 288*A + B, 688*A + B, 888*A + B where A = 10^(n-3), B = 8*(A - 1)/9.
%F From _M. F. Hasler_, Jun 23 2020: (Start)
%F a(n) = 10*a(n-7) + 8 for n > 13 (and with a(n-6) for 7 < n < 13).
%F G.f.: (1 + x + 4*x^2 + 2*x^3 + 2*x^4 + 8*x^5 + 2*x^6 - 2*x^7 + 30*x^8 - 20*x^9 + 60*x^11 - 68*x^12 - 12*x^13)/((1 - x)*(1 - x^10)).
%F (End)
%F a(n) = a(n-1) + 10*a(n-7) - 10*a(n-8), for n >= 15. - _Wesley Ivan Hurt_, Jun 29 2020
%e Digits 0, 1, 2, ..., 9 use 6, 2, 5, 5, 4, 5, 6, 3, 7, 6 lines / segments.
%t Block[{f, s}, MapIndexed[(f[#2[[1]] - 1] = #1) &, {6, 2, 5, 5, 4, 5, 6, 3, 7, 6}]; s = Array[Total[f /@ IntegerDigits[#]] &, 10^7]; Map[FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* or *)
%t Nest[Append[#1, If[#2 > 13, 10 #1[[-7]] + 8, 10 #1[[-6]] + Boole[#2 != 13] 8]] & @@ {#, Length@ # + 1} &, {1, 2, 6, 8, 10, 18, 20}, 36] (* _Michael De Vlieger_, Jun 23 2020 *)
%o (PARI) apply( {A038619(n)=if(n>7, self()(n-6-(n>13))*10+(n!=13)*8, [1,2,6, 8,10,18,20][n])}, [1..33]) \\ _M. F. Hasler_, Jun 23 2020
%Y Cf. A143617, A216261; A234691, A234692; A277116, A074458, A006942, A010371, A063720.
%K nonn,base,easy,nice
%O 1,2
%A _Jan Kristian Haugland_
%E Edited and offset corrected to 1 by _M. F. Hasler_, Jun 23 2020
%E More terms from _Michael De Vlieger_, Jun 23 2020
%E More terms from _M. F. Hasler_, Jun 23 2020
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