A006942 -id:A006942 - cp's OEIS frontend

A386910 Number of iterations of seven segments count x -> A063720(x) to go from n to a fixed point.

2, 2, 1, 1, 0, 0, 1, 2, 3, 1, 4, 1, 3, 3, 2, 3, 3, 1, 2, 3, 2, 3, 5, 5, 2, 5, 5, 4, 4, 5, 2, 3, 5, 5, 2, 5, 5, 4, 4, 5, 5, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 3, 5, 5, 2, 5, 5, 4, 4, 5, 2, 3, 5, 5, 2, 5, 5, 4, 4, 5, 2, 1, 4, 4, 3, 4, 4, 2, 5, 4, 4, 2, 4, 4, 2, 4, 4

Offset: 0

Marco Ripà, Aug 07 2025

A063720 is a strictly decreasing function A063720(x) < x whenever x >= 10 and all single digit x reach a fixed point A063720(x) = x with x in {4, 5}.

This sequence is unbounded and the first occurrence of a(n) = k is at n = A338255(k + 1) for any k >= 3.

			For n = 12, the a(12) = 3 steps are 12 -> 7 -> 3 -> 5 segments, and 5 is a fixed point A063720(5) = 5.

Cf. A063720, A328330, A338255, A385249.

Cf. A006942, A010371, A074458, A277116 (segments variation).

A123587 Number of bars that must change on a standard digital clock when the minutes change from n-1 to n.

Original entry on oeis.org

5, 4, 5, 2, 3, 3, 1, 5, 4, 1, 6, 4, 5, 2, 3, 3, 1, 5, 4, 1, 7, 4, 5, 2, 3, 3, 1, 5, 4, 1, 4, 4, 5, 2, 3, 3, 1, 5, 4, 1, 5, 4, 5, 2, 3, 3, 1, 5, 4, 1, 5, 4, 5, 2, 3, 3, 1, 5, 4, 1, 5, 4, 5, 2, 3, 3, 1, 5, 4, 1, 6, 4, 5, 2, 3, 3, 1, 5, 4, 1, 7, 4, 5, 2, 3, 3, 1, 5, 4, 1, 4, 4, 5, 2, 3, 3, 1, 5, 4, 1, 5, 4, 5, 2, 3, 3, 1, 5, 4, 1, 5, 4, 5, 2, 3, 3, 1, 5, 4, 1

Offset: 0

Danny Rorabaugh, Nov 13 2006

Cyclic with period 60.

			a(20)=7 because when the clock changes from 19 to 20 minutes, 1 bar turns off and 4 bars turn on in the tens digit for the "0" to become a "1" and 1 bar turns off and 1 turns on in the units digit for the "9" to become a "0". 1 + 4 + 1 + 1 = 7.

Cf. A006942, A010371, A063720.

A165244 The numbers commonly displayed with 7 segments in electric clocks, in ascending order of number of segments lit.

Original entry on oeis.org

1, 7, 4, 2, 3, 5, 0, 6, 9, 8

Offset: 1

Kurt Eisemann (keiseman(AT)mail.sdsu.edu), Sep 09 2009

Curiosity Show, Tricky Numerals: Your Number's Up!, YouTube video, 1982.

Cf. A006942, A074458, A010371.

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]]

A339700 a(n) is the n-th nonnegative number to light exactly n segments when displayed on a calculator.

Original entry on oeis.org

71, 77, 47, 61, 70, 52, 62, 99, 136, 190, 246, 263, 306, 589, 882, 1085, 1838, 2059, 2308, 2869, 5886, 8689, 10800, 18098, 20268, 20896, 28608, 58880, 86886, 106898, 180889, 200858, 208698, 283888, 588868, 868880, 1068889, 1808886, 2008086, 2086868, 2809888, 5888808, 8688868, 10688886, 18088880

Offset: 5

Graham Holmes, Dec 13 2020

a(n) is undefined for n<5, as there are no numbers with 1 segment, 1 with 2 segments, 1 with 3 segments, and 2 with 4 segments. If 0 is excluded as a valid input - so the series would refer to "the n-th positive number" - then a(6) would be 111 rather than 77.

			For n=7, 47 is the 7th positive number to light 7 segments, after 8, 12, 13, 15, 21, and 31.

Graham Holmes, Table of n, a(n) for n = 5..82
Index entries for sequences related to calculator display

Cf. A006942 (segments lit), A216261, A331529.

s=[6,2,5,5,4,5,6,3,7,6];p=[];a=[];for(i=2;i<=100;i++)p[i]=0;for(i=1;i<=1000000;i++){d=i;n=0;do{x=d%10;n+=s[x];d=(d-x)/10;}while(d>0)p[n]++;if(p[n]==n)a[n]=i;}for(c=2;c<=40;c++)document.write(c+": "+a[c]+"
");

A345972 Numbers that are integer multiples of the count of active segments in their 7-segment-display form where '6', '7' and '9' use 6, 3 and 6 segments, respectively.

Original entry on oeis.org

0, 4, 5, 6, 16, 18, 21, 40, 45, 54, 60, 72, 81, 96, 110, 130, 132, 143, 154, 156, 176, 180, 182, 195, 196, 224, 225, 238, 240, 255, 256, 273, 306, 312, 320, 336, 341, 384, 400, 405, 408, 420, 442, 444, 450, 451, 465, 481, 495, 496, 518, 525, 540, 555, 572, 592

Offset: 1

Marian Aldenhövel and Florentin Aldenhövel, Jun 30 2021

The sequence is given for 7-segment displays that format their digits like so:
                               
  | | |  |  |  || |  |    | || |_|
  || | |   |    |  | ||   | ||  _|
.
This sequence is infinite: For any n let e := Sum_{i=0..n} 2*4^i (2, 10, 42, ... see A020988). The number a := 4*10^e is a member of the sequence. It has 4+6*e active segments (one four and e noughts).
The numbers 4, 5 and 6 are the only entries that exactly equal their count of active segments.

Heureka - Mathematische Rätsel 2021 - Tageskalender, Anaconda-Verlag, 2020, ISBN-978-3-7306-0881-4.

Marian Aldenhövel, Table of n, a(n) for n = 1..10000
Index entries for sequences related to calculator display

Cf. A006942, A020988.

def filter(n):
    seg = 0
    for c in str(n):
        seg += { 0: 6, 1: 2, 2: 5, 3: 5, 4: 4, 5: 5, 6: 6, 7: 3, 8: 7, 9: 6 }[int(c)]
    return(n % seg == 0)

A387106 Number of iterations of seven segments count x -> A074458(x) to go from n to a fixed point.

Original entry on oeis.org

1, 2, 1, 1, 0, 0, 0, 1, 2, 1, 3, 1, 2, 2, 1, 2, 3, 1, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 3, 4, 2, 2, 4, 4, 2, 4, 2, 2, 3, 4, 4, 1, 2, 2, 3, 2, 4, 3, 2, 2, 2, 2, 4, 4, 2, 4, 2, 2, 3, 4, 3, 3, 2, 2, 4, 2, 3, 4, 3, 2, 4, 1, 2, 2, 3, 2, 4, 3, 2, 2, 3, 2, 3, 3, 2, 3, 3

Offset: 0

Marco Ripà, Aug 16 2025

A074458 is a strictly decreasing function A063720(x) < x whenever x >= 10 and all single digit x reach a fixed point A063720(x) = x with x in {4, 5}.

This sequence is unbounded and the first occurrence of a(n) = k is at n = A338255(k + 2) for any k >= 3.

			For n = 10, the a(10) = 3 steps are 10 -> 8 -> 7 -> 4 segments, and 4 is a fixed point A074458(4) = 4.

Wikipedia, Seven-segment display.

Cf. A074458, A328330, A385249, A386910.

Cf. A006942, A010371, A063720, A277116 (segments variation).

A071843 Gives an LCD representation of n.

Original entry on oeis.org

119, 17, 107, 59, 29, 62, 126, 19, 127, 63, 15249, 2193, 13713, 7569, 3729, 7953, 16145, 2449, 16273, 8081, 15339, 2283, 13803, 7659, 3819, 8043, 16235, 2539, 16363, 8171, 15291, 2235, 13755, 7611, 3771, 7995, 16187, 2491, 16315, 8123, 15261, 2205

Offset: 0

Anonymous, Jun 08 2002

This is based on the following way of writing "8":
|--2--|
4.....1
|--8--|
64...16
|-32--|
The powers of 2 present in the LCD representation are added. For example: n=1 gives 1 + 16 = 17. According to the position of a digit in n, [1,2,4...] is replaced by [128,256...],[16384,32768...], etc.

Cf. A006942 (bitcount).

Coding and glyph variations: A234691, A234692.

function lcd: nb: final result ndc: number of digits u: interesting digit M(i,j): (j-1)th bit of (i-1) function [nb]=lcd(n); nb=0; M=[1 1 1 0 1 1 1; 1 0 0 0 1 0 0; 1 1 0 1 0 1 1; 1 1 0 1 1 1 0; 1 0 1 1 1 0 0; 0 1 1 1 1 1 0; 0 1 1 1 1 1 1; 1 1 0 0 1 0 0; 1 1 1 1 1 1 1; 1 1 1 1 1 1 0]; if n <> 0 then ndc=int(log10(n))+1,else ndc = 1,end; for cx = ndc:-1:1; u=int(n/(10^(cx-1))); n=n-u*(10^(cx-1)); for j=0:6; nb=nb+M(u+1,j+1)*2^(j+7*(ndc-cx)),end,end; endfunction

More terms from Antonio G. Astudillo, Apr 21 2003

A309721 Number of right angles between the segments that are turned "on" when representing n on a 7-segment (calculator) display.

Original entry on oeis.org

4, 0, 4, 4, 3, 4, 6, 1, 8, 6, 4, 0, 4, 4, 3, 4, 6, 1, 8, 6, 8, 4, 8, 8, 7, 8, 10, 5, 12, 10, 8, 4, 8, 8, 7, 8, 10, 5, 12, 10, 7, 3, 7, 7, 6, 7, 9, 4, 11, 9, 8, 4, 8, 8, 7, 8, 10, 5, 12, 10, 10, 6, 10, 10, 9, 10, 12, 7, 14, 12, 5, 1, 5, 5, 4, 5, 7, 2, 9, 7, 12, 8, 12, 12, 11, 12, 14, 9, 16, 14, 10, 6, 10, 10, 9, 10, 12, 7

Offset: 0

Ivan N. Ianakiev, Aug 14 2019

The display is the one described in A006942 (see also the example section below).

			To illustrate a(0),...,a(9):
   _     _  _       _   _   _   _   _
  | | |  _| _| |_| |_  |_    | |_| |_|
  |_| | |_  _|   |  _| |_|   | |_|  _|
.

Cf. A006942, A010371, A063720, A277116.

Evaluate[Table[a[n],{n,0,9}]]={4,0,4,4,3,4,6,1,8,6};
a[n_/;n>9]:=a[Floor[n/10]]+a[Mod[n,10]]; a/@Range[0,100] (* or *)
Table[Total[IntegerDigits[n]/.{0->4,1->0,2->4,3->4,4-> 3,5->4,7->1,9->6}],{n,0,100}]

a(n) = a(floor(n/10)) + a(n mod 10), for n > 9 (a formula by Reinhard Zumkeller, same for A006942 and A010371).

A386244 Number of iterations of seven segments count x -> A277116(x) to go from n to a fixed point.

Original entry on oeis.org

1, 2, 1, 1, 0, 0, 0, 2, 3, 1, 4, 1, 3, 3, 1, 3, 4, 1, 2, 3, 2, 3, 5, 5, 2, 5, 2, 4, 4, 5, 2, 3, 5, 5, 2, 5, 2, 4, 4, 5, 5, 1, 2, 2, 4, 2, 5, 3, 2, 2, 2, 3, 5, 5, 2, 5, 2, 4, 4, 5, 4, 4, 2, 2, 5, 2, 4, 2, 4, 2, 2, 1, 4, 4, 3, 4, 2, 1, 5, 4, 4, 2, 4, 4, 2, 4, 4, 5, 2, 4

Offset: 0

Marco Ripà, Aug 21 2025

A277116 a strictly decreasing function A277116(x) < x whenever x >= 10 and all single digit x reach a fixed point A277116(x) = x with x in {4, 5, 6}.

This sequence is unbounded and the first occurrence of a(n) = k is at n = A338255(k + 1) for any k >= 3.

			For n = 10, the a(10) = 3 steps are 10 -> 8 -> 7 -> 3 -> 5 segments, and 5 is a fixed point A074458(5) = 5.

Wikipedia, Seven-segment display.

Cf. A277116, A328330, A385249, A386910, A387106.

Cf. A006942, A010371, A063720, A074458 (segments variation).

cp's OEIS Frontend

A386910 Number of iterations of seven segments count x -> A063720(x) to go from n to a fixed point.

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A123587 Number of bars that must change on a standard digital clock when the minutes change from n-1 to n.

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A165244 The numbers commonly displayed with 7 segments in electric clocks, in ascending order of number of segments lit.

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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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Mathematica

A339700 a(n) is the n-th nonnegative number to light exactly n segments when displayed on a calculator.

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JavaScript

A345972 Numbers that are integer multiples of the count of active segments in their 7-segment-display form where '6', '7' and '9' use 6, 3 and 6 segments, respectively.

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A387106 Number of iterations of seven segments count x -> A074458(x) to go from n to a fixed point.

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A071843 Gives an LCD representation of n.

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A309721 Number of right angles between the segments that are turned "on" when representing n on a 7-segment (calculator) display.

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Formula

A386244 Number of iterations of seven segments count x -> A277116(x) to go from n to a fixed point.

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