

A234692


Decimal value of the bitmap of active segments in 7segment display of the number n, variant 2 ("abcdefg" scheme: bits represent segments in clockwise order).


11



63, 6, 91, 79, 102, 109, 125, 39, 127, 111, 831, 774, 859, 847, 870, 877, 893, 807, 895, 879, 11711, 11654, 11739, 11727, 11750, 11757, 11773, 11687, 11775, 11759, 10175, 10118, 10203, 10191, 10214, 10221, 10237, 10151, 10239, 10223, 13119, 13062, 13147, 13135, 13158
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OFFSET

0,1


COMMENTS

The bits 06 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 segmenttobit 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 base10 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 7segment variant of the characters AZ and/or az, as in hexadecimal or base64 encoding. In that case, one could also use a few more bits for additional segments, e.g., four halfdiagonals 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 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


LINKS

Table of n, a(n) for n=0..44.
Wikipedia, Sevensegment display.


FORMULA

a(n) = a(n%10) + a(floor(n/10))*2^7, where % is the remainder operator.  M. F. Hasler, Jun 17 2020


EXAMPLE

a(7) = 39 = 2^0 + 2^1 + 2^2 + 2^5, because the digit 7 is represented as
" _ " : bit 0,
" " : bits 5+1,
" " : bit 2,
and no bit 3 (bottom "_") nor 4 (lower left "") nor 6 (central "").
Although other glyphs do exist as well for 6, 9, 0 and maybe other digits, "7" is probably the digit where an alternate representation (without the upper left "") is as common as the one we chose here.


PROG

(PARI) bitmap=apply(s>sum(i=1, #s=Vec(s), if(s[i]>" ", 2^(i1))), ["000000", " 11", "22 22 2", "3333 3", " 44 44", "5 55 55", "6 66666", "777 7", "8888888", "9999 99", "AAA AAA", " bbbbb", "C CCC ", " dddd d", "E EEEE", "F FFF"]) \\ Could be extended to more alphabetical glyphs, see A234691.
apply( {A234692(n)=bitmap[n%10+1]+if(n>9, self()(n\10)<<7)}, [0..99]) \\M. F. Hasler, Jun 17 2020


CROSSREFS

Cf. A234691 for a variant where bits 06 represent, in this order, the segments: top, upper left, upper right, center, lower left, lower right, bottom.
Cf. A000120 (Hamming weight), A010371 and variants A063720, A277116, A074458 and A006942: see comments.
Sequence in context: A324018 A102241 A255915 * A339458 A084507 A202157
Adjacent sequences: A234689 A234690 A234691 * A234693 A234694 A234695


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Dec 29 2013


EXTENSIONS

Extended with hex digits (AbCdEF) to n=15 by M. F. Hasler, Dec 30 2013
a(10) and a(11) corrected thanks to Kevin Ryde, M. F. Hasler, Jun 16 2020
Changed definition for consistency with A010371 etc.  M. F. Hasler, Jun 17 2020


STATUS

approved



