cp's OEIS Frontend

a(A216261(n)) = n and a(m) <> n for m < A216261(n). - Reinhard Zumkeller, Mar 15 2013

If we mark with * resp. ' the graphical representations which use more resp. less segments, we have the following variants:

A063720 (6', 7', 9'), A277116 (6*, 7', 9'), A074458 (6*, 7*, 9'),

_____________ this: 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

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

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

| | |

| (here), vs. | in A006942.

If we mark with ' the "sans serif" graphical representation which uses one segment less and with * the "heavier" version, we have the following variants:

A063720 (6', 7', 9'), A277116 (6*, 7', 9'), A074458 (6*, 7*, 9'),

___________________ A006942 (6*, 7', 9*), A010371 (6*, 7*, 9*) = this.

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

If we mark with * resp. ' the glyph variants (graphical representations) which use more resp. less segments, we have the following variants:

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

Sequences A234691 and A234692 use one bit for each lit segment. See crossrefs for other variants. - M. F. Hasler, Jun 17 2020

Another version of A006942. Here the digit "6" is represented with six segments (the same as in A006942) but the digit "9" is represented with five segments instead of six segments. - Omar E. Pol, Sep 30 2016

If we mark with * resp. ' the graphical representations which use one more resp. one less segment, we have the following variants:

A063720 (6', 7', 9'), A277116 (6*, 7', 9'), A074458 (6*, 7*, 9'),

___________________ A006942 (6*, 7', 9*), A010371 (6*, 7*, 9*).

Sequences A234691 and A234692 make precise which segments are lit in each digit. They are related through the Hamming weight function A000120, e.g., A010371(n) = A000120(A234691(n)) = A000120(A234692(n)). - M. F. Hasler, Jun 17 2020

The bits 0-6 are assigned to the segments according to the "abcdefg" scheme (top, upper right, lower right, bottom, lower left, upper left, center), cf. section "Displaying letters" of the Wikipedia page (3rd column of the table). Other conventions are common in engineering (as well for the segment-to-bit correspondence as for the glyphs), see sequence A234691, the Wikipedia page and the comment after the Example for a(7).

For n > 9, each of the digits of the base-10 representation is coded in a separate group of 7 bits, for example, a(10) = a(1)*2^7 + a(0) = 831.

Alternatively, for n >= 10 one could define a(n) to represent a 7-segment variant of the characters A-Z and/or a-z, as in hexadecimal or base-64 encoding. In that case, one could also use a few more bits for additional segments, e.g., four half-diagonals to represent K, M, N, R, V, X, Z correctly and S distinctly from 5. But as mentioned on the Wikipedia page, a possible ambiguity of representations of alphabetic characters is not always an obstacle to common use, since whole words are usually readable nonetheless.

The Hamming weight A000120 of the terms of this sequence yields the count of lit segments, A010371(n) = A000120(a(n)) = A000120(A234691(n)). For that sequence, 5 other variants are in the OEIS, depending on the number of segments used to represent digits 6, 7 and 9: A063720 (6', 7', 9'), A277116 (7', 9'), A074458 (9') and A006942 (7'), where x' means that the "sans serif" variant (one segment less than here) is used for digit x. - M. F. Hasler, Jun 17 2020

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

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

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.

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.