A038619 -id:A038619 - cp's OEIS frontend

A216261 Smallest positive number using exactly n segments on a calculator display (when '6' and '7' are represented using 6 resp. 3 segments).

1, 7, 4, 2, 0, 8, 10, 18, 22, 20, 28, 68, 88, 108, 188, 200, 208, 288, 688, 888, 1088, 1888, 2008, 2088, 2888, 6888, 8888, 10888, 18888, 20088, 20888, 28888, 68888, 88888, 108888, 188888, 200888, 208888, 288888, 688888, 888888, 1088888, 1888888, 2008888, 2088888, 2888888

Offset: 2

Reinhard Zumkeller, Mar 15 2013

Essentially the same as A038619 and A143617. One could argue that a(3) should rather be -1 (prior to adding "positive" in the definition), which does use 3 segments on typical 7-segment displays, and is smaller than 7. Also, most pocket calculators and the Unicode standard (cf. links) use 4 rather than 3 segments to represent a '7' (as in A074458 and A010371, rather than A063720, A277116 or A006942), in which case a(3) is undefined if negative numbers are not allowed. No digit '9' will ever occur here, whether it would be represented with 6 or only 5 segments. However, digit '6' does occur, as the second smallest digit using 6 segments as does '0', which cannot occur as leading digit. If '6' is represented with 5 segments, any prefix 68 would be replaced with 80. - M. F. Hasler and Kevin Ryde, Jun 17 2020

Unicode, Symbols for Legacy Computing, The Unicode Standard, Version 13.0, 2020.
Index entries for sequences related to calculator display
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,10,-10).

Cf. A006942, A010371, A063720, A074458, A277116; A234691, A234692.

Cf. A038619 and A143617 (identical up to initial terms).

import Data.Maybe (fromJust)
import Data.List (elemIndex)
a216261 = fromJust . (`elemIndex` a006942_list)
-- Reinhard Zumkeller, Mar 15 2013

Drop[#, 2] &@ CoefficientList[Series[(x^2 + 6 x^3 - 3 x^4 - 2 x^5 - 2 x^6 + 8 x^7 + 2 x^8 - 2 x^9 - 56 x^10 + 28 x^11 + 28 x^12 + 60 x^13 - 60 x^14 - 28 x^17 + 28 x^18)/((1 - x) (1 - 10 x^7)), {x, 0, 50}], x] (* Michael De Vlieger, Jan 29 2016 *)

Vec((x^2 +6*x^3 -3*x^4 -2*x^5 -2*x^6 +8*x^7 +2*x^8 -2*x^9 -56*x^10 +28*x^11 +28*x^12 +60*x^13 -60*x^14 -28*x^17 +28*x^18)/((1-x)*(1-10*x^7)) + O(x^50)) \\ Michel Marcus, Jan 29 2016

A006942(a(n)) = n and A006942(m) <> n for m < a(n).
a(n+7) = 10*a(n) + 8 for n > 10. This can be deduced from a(n) = min{10*a(n-A006942(r))+r, r=0..9} via strong induction. - David Radcliffe, Jan 29 2016
G.f.: (x^2 +6*x^3 -3*x^4 -2*x^5 -2*x^6 +8*x^7 +2*x^8 -2*x^9 -56*x^10 +28*x^11 +28*x^12 +60*x^13 -60*x^14 -28*x^17 +28*x^18)/((1-x)*(1-10*x^7)). - David Radcliffe, Jan 29 2016

Name and cross-references edited by M. F. Hasler, Jun 17 2020

A143617 Where record values occur in A010371.

Original entry on oeis.org

0, 8, 10, 18, 20, 28, 68, 88, 108, 188, 200, 208, 288, 688, 888, 1088, 1888, 2008, 2088, 2888, 6888, 8888, 10888, 18888, 20088, 20888, 28888, 68888, 88888, 108888, 188888, 200888, 208888, 288888, 688888, 888888, 1088888, 1888888, 2008888, 2088888

Offset: 1

Reinhard Zumkeller, Aug 27 2008

nonn

a(n) is the least number using n + 6 (or n + 5 for n < 5) segments on a 7-segment display, when '6' uses 6 segments. This is essentially the same as A038619 (starts with 1, 2, 6 instead of 0) and A216261 (= a(n) uses n segments: has 4 values before 0 and 22 before 20). - M. F. Hasler, Jun 17 2020

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,10,-10).

Cf. A010371, A143616.

Block[{f, s}, MapIndexed[(f[#2[[1]] - 1] = #1) &, {6, 2, 5, 5, 4, 5, 6, 4, 7, 6}]; s = Array[Total[f /@ IntegerDigits[#]] &, 10^6, 0]; Map[-1 + FirstPosition[s, #][[1]] &, Union@ FoldList[Max, s]]] (* Michael De Vlieger, Jun 23 2020 *)

apply( {A143617(n)=if(n>11,self()(n-7)*10+8, n>9, 12*n+68, n>6, 20*n-72, n*5-2-n%2*3)}, [1..55]) \\ M. F. Hasler, Jun 23 2020

a(n+7) = 10*a(n) + 8 for n > 4.
A010371(a(n)) = A143616(n) and A010371(m) < A143616(n) for m < a(n).
A010371(a(n)) = n + 6 for n > 4. - M. F. Hasler, Jun 23 2020
a(n) = a(n-1) + 10*a(n-7) - 10*a(n-8). - Wesley Ivan Hurt, Jul 03 2020

A338111 Times displayed on an hour|minute 12-hour 7-segment digital clock, arranged in order of increasing brightness (see Comments).

Original entry on oeis.org

111, 117, 711, 114, 141, 411, 717, 1111, 112, 113, 115, 121, 131, 147, 151, 211, 311, 417, 511, 714, 741, 1117, 101, 110, 116, 119, 127, 137, 144, 157, 217, 317, 414, 441, 517, 611, 712, 713, 715, 721, 731, 747, 751, 911, 1114, 1141, 107, 118, 124, 134, 142

Offset: 1

Harvey P. Dale, Oct 10 2020

Consider a 12-hour digital clock with 4 digits, each of which comprises 7 facets (or segments or lights). The terms of the sequence list the times of day starting with the dimmest overall display, i.e., when the fewest total facets are lit up, to the brightest overall display, i.e., when the most total facets are lit up.The terms are sorted by dimness/brightness and then by smallest-to-largest number.
If the digits are labeled A, B, C, D from left to right, digit A is completely dark from 1:00 until after 9:59, and then has 2 facets lit up from 10:00 through 12:59. Digits B and D will each display numbers from 0 to 9 and thus will have between 2 and 7 facets lit up. Digit C will display numbers from 0 to 5 and thus will have between 2 and 6 facets lit up.
The sequence displays each time of day without the customary colon separating hours from minutes, so for example 12:36 is displayed as 1236 and 9:14 is displayed as 914.
The dimmest display is for 1:11 (or 111) when 6 facets in total are lit up. The brightest display is for 10:08 (or 1008) when 21 facets are lit up. The sequence has 720 terms altogether.

			111 is displayed with digit A dark and with 2 facets of each of digits B, C, and D lit up. Thus 111 has a total of 6 facets lit up. 1008 is displayed with 2 facets of digit A lit up, with 6 facets of digits B and C lit up, and with 7 facets of digit D lit up. Thus 1008 has a total of 21 facets lit up.

Harvey P. Dale, Table of n, a(n) for n = 1..720

Cf. A006942, A038619, A063720, A074458, A123587, A277116, A234691, A234692.

SortBy[{#,Total[IntegerDigits[#]/.{0->6,1->2,2->5,3->5,7->3,8->7,9->6}]}&/@ FromDigits/@Flatten[Table[Join[IntegerDigits[ h],PadLeft[ IntegerDigits[ m],2,0]],{h,12},{m,0,59}],1],{Last,First}][[All,1]]

cp's OEIS Frontend

A216261 Smallest positive number using exactly n segments on a calculator display (when '6' and '7' are represented using 6 resp. 3 segments).

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A143617 Where record values occur in A010371.

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A338111 Times displayed on an hour|minute 12-hour 7-segment digital clock, arranged in order of increasing brightness (see Comments).

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