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A234691
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Decimal value of the bitmap of active segments in 7-segment display of the number n, variant 1: bits 0-6 refer to segments from top to bottom, left to right.
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11
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119, 36, 93, 109, 46, 107, 123, 39, 127, 111, 4727, 4644, 4701, 4717, 4654, 4715, 4731, 4647, 4735, 4719, 12023, 11940, 11997, 12013, 11950, 12011, 12027, 11943, 12031, 12015, 14071, 13988, 14045, 14061, 13998, 14059, 14075, 13991, 14079, 14063, 6007, 5924, 5981, 5997
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OFFSET
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0,1
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COMMENTS
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The bits 0-6 are assigned to the segments as follows: top (bit 0), upper left, upper right, middle, lower left, lower right, bottom (bit 6). Other conventions are common in engineering (as well for the segment-to-bit correspondence as for the glyphs), see sequence A234692 (the so-called ABCDEF coding), Wikipedia and the Example for a(7).
For n > 9, the decimal representation of n is encoded using a group of 7 bits for each digit, e.g., a(10) = a(1)*2^7 + a(0).
The sequence could have been extended differently to indices > 9, for example, by coding 7-segment representations of upper- and/or lowercase letters, as used for hexadecimal and base-64 representation.
The Hamming weight A000120 of the terms of this sequence yields the count of lit segments, A010371(n) = A000120(A234691(n)) = A000120(A234692(n)). For that sequence, 4 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
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LINKS
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FORMULA
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a(n) = a(n mod 10) + a(floor(n/10))*2^7 for n > 9. - M. F. Hasler, Jun 17 2020
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EXAMPLE
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The digits are assumed to be rendered as follows:
_ _ _ _ _ _ _ _
| | | _| _| |_| |_ |_ | | |_| |_|
|_| | |_ _| | _| |_| | |_| _|
For example, a(7) = 39 = 2^0 + 2^1 + 2^2 + 2^5, because the nonzero bits are
_ : bit 0,
| | : bits 1+2,
| : bit 5,
while bits 3 (central '-'), 4 (lower left '|') and 6 (bottom '_') remain 0.
For the digit '7', the "sans serif" representation (without the upper left '|') is also very common; it would correspond to a(7) = 37. Similarly, digits 6 and 9 are sometimes represented without the top resp. bottom bar, see comments.
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PROG
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(PARI) /* Bitmaps computed from 7-character strings. Extended beyond 9 with characters most frequently used to code hexadecimal digits A-F, chessboard coordinates a-h, and other letters. Alternate glyphs used more or less frequently: sans serif " 6 6666", "7 7 7 ", "9999 9 "; "a aaaaa", B same as 8, "eeeee e", g same as 9, H same as X, "i i i" or " i ", "J J JJJ" or "J J JJ", S same as 5, "TT T ", " YYY Y ". Note: Z below is the same as 2! */
bitmaps = { apply( s2b = s->sum(i=1, #s=Vec(s), if(s[i]>" ", 2^(i-1))), ["000 000", " 1 1 ", "2 222 2", "3 33 33", " 444 4 ", "55 5 55", "66 6666", "777 7 ", "8888888", "9999 99", "AAAAAA ", " b bbbb", "CC CC", " ddddd",
"EE EEEE", "FF FF ", "GG GGG", " h hhh ", " I I ", " J JJ", "KK KKK ",
" L L L", "MMM MM ", " nnn ", " oooo", "PPPPP ", "qqqq q ", " rr ", " s ss", " t tt t", " uuu", " VV VVV", " XXXXX ", " YYY YY", "Z ZZZ Z"])} \\ Extended to letters by M. F. Hasler, Jun 16 2020
apply( {A234691(n)=bitmaps[n%10+1]+if(n>9, self()(n\10)<<7)}, [0..99]) \\ Extended to n > 9 by M. F. Hasler, Jun 17 2020
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CROSSREFS
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Cf. A234692 for the "abcdefg" coding variant (clockwise from top and ending with bit 6 for the central "-").
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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