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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

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

apply( {A234692(n)=bitmap[n%10+1]+if(n>9, self()(n\10)<<7)}, [0..99]) \\_ _M. F. Hasler_, Jun 17 2020

Changed definition Definition changed for consistency with A010371 , etc. - _by _M. F. Hasler_, Jun 17 2020

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Alternatively, for n >= 10 one could define a(n) to represent a 7-segment variant of the characters A-Z and/or a-z, for n >= 10, 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.

One could also use The Hamming weight A000120 of the terms of this sequence yields the count of lit segments, A010371(n) = A000120(a few more bits for additional (n)) = A000120(A234691(n)). For that sequence, 5 other variants are in OEIS, depending on the number of segments, e.g., four half-diagonals used to represent K, M, N, R, V, X, Z correctly digits 6, 7 and 9: A063720 (6', 7', 9'), A277116 (7', 9'), A074458 (9') and S distinctly from 5. But as mentioned on A006942 (7'), where x' means that the Wikipedia page, a possible ambiguity of representations of alphabetic characters "sans serif" variant (one segment less than here) is not always an obstacle to common use, since whole words are usually readable nonethelessused for digit x. - _M. F. Hasler_, Jun 17 2020

Applying the Hammingweight function A000120 to the terms of this sequence, one gets 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

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Applying the Hammingweight function A000120 to the terms of this sequence, one gets the count of lit segments, A010371(n) = A000120(A234691a(n)) = A000120(A234692A234691(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

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

63, 6, 91, 79, 102, 109, 125, 39, 127, 111, 119, 124, 57, 94, 121, 113831, 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

(PARI) A234692bitmap=apply(s->sum(i=1, #s=Vec(s), if(s[i]>" ", 2^(i-1))), ["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. - _M. F. Hasler_, Jun 16 2020

apply( {A234692(n)=bitmap[n%10+1]+if(n>9, self()(n\10)<<7)}, [0..99]) \\M. F. Hasler, Jun 17 2020

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

The terms 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) through = a(1)*2^7 + a(150) correspond to A-F commonly used in hexadecimal= 831.

The sequence is currently labeled "fini(te), full", but it Alternatively, one could be extended define a(n) to represent a 7-segment variant of the characters A-Z and/or a-z, for n >= 10, as in several ways:hexadecimal or base-64 encoding.

1) Arbitrary large integers > 9 One could be represented as multi-digit numbers by using as many groups of 7 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 there 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 digits: for example, a(10) would then be a(1)*2^7 + a(0) = 831usually readable nonetheless.

2) The extension suggested by Applying the Hammingweight function A000120 to the terms of this sequence, one gets the current acount of lit segments, A010371(n) = A000120(A234691(10n))-a = A000120(A234692(15n)) would consist . For that sequence, 5 other variants are in extending it OEIS, depending on the number of segments used to 10+26 or 10+26*2 with codes for glyphs A-Z represent digits 6, 7 and 9: A063720 (6', 7', 9'), A277116 (7', 9'), A074458 (9') and/or a-z, possibly ambiguous. A006942 (As mentioned on 7'), where x' means that the Wikipedia page, a possible ambiguity of representations of alphabetic characters "sans serif" variant (one segment less than here) is not an obstacle to common use, since whole words are usually readable nonethelessused for digit x. - _M. F.) Hasler_, Jun 17 2020

3) 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. [Edited by M. F. Hasler, Jun 16 2020]

Cf. A000120 (Hamming weight), A010371 and variants A063720, A277116, A074458 and A006942: see comments.

nonn,base,fini,full,changed

nonn,base

Changed definition for consistency with A010371 etc. - M. F. Hasler, Jun 17 2020

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