A102679 -id:A102679 - cp's OEIS frontend

A006942 Number of segments used to represent n on calculator display, variant 5: digits '6', '7' and '9' use 6, 3 and 6 segments, respectively.

6, 2, 5, 5, 4, 5, 6, 3, 7, 6, 8, 4, 7, 7, 6, 7, 8, 5, 9, 8, 11, 7, 10, 10, 9, 10, 11, 8, 12, 11, 11, 7, 10, 10, 9, 10, 11, 8, 12, 11, 10, 6, 9, 9, 8, 9, 10, 7, 11, 10, 11, 7, 10, 10, 9, 10, 11, 8, 12, 11, 12, 8, 11, 11, 10, 11, 12, 9, 13, 12, 9, 5, 8, 8, 7, 8, 9

Offset: 0

N. J. A. Sloane

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

			As depicted below, zero uses 6 segments, so a(0)=6.
   _     _  _       _   _   _   _   _
  | | |  _| _| |_| |_  |_    | |_| |_|
  |_| | |_  _|   |  _| |_|   | |_|  _|
.
[Edited by _Jon E. Schoenfield_, Jul 30 2017]

Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 65.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Nathaniel Johnston, Table of n, a(n) for n = 0..10000
Netnews group rec.puzzles, Frequently Asked Questions (FAQ) file, Instructions problem series.31, and Series Section solution series.31.
Index entries for sequences related to calculator display

Cf. A216261 (least inverse), A165244 (sorted digits), A302552 (primes), A328330 (iterations), A331529 (histogram).
Variants are A010371, A063720, A074458, A277116, see comments.
See also A234691, A234692, A000120.

a006942 n = a006942_list !! n
a006942_list = [6,2,5,5,4,5,6,3,7,6] ++ f 10 where
   f x = (a006942 x' + a006942 d) : f (x + 1)
         where (x',d) = divMod x 10
-- Reinhard Zumkeller, Mar 15 2013

A006942 := proc(n) local d,dig,j,s: if(n=0)then return 6:fi: dig:=[6,2,5,5,4,5,6,3,7,6]: d:=convert(n,base,10): s:=0: for j from 1 to nops(d) do s:=s+dig[d[j]+1]: od: return s: end: seq(A006942(n),n=0..100); # Nathaniel Johnston, May 08 2011

MapIndexed[ (f[First[#2] - 1] = #1)& , {6, 2, 5, 5, 4, 5, 6, 3, 7, 6}]; a[n_] := Plus @@ f /@ IntegerDigits[n]; Table[a[n], {n, 0, 76}] (* Jean-François Alcover, Sep 25 2012 *)
a[n_] := Plus @@ (IntegerDigits@ n /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 7 -> 3, 8 -> 7, 9 -> 6}); Array[a, 77, 0] (* Robert G. Wilson v, Jun 20 2018 *)

a(n)=if(n==0, return(6)); my(d=digits(n),v=vector(10)); for(i=1,#d, v[d[i]+1]++); v*[6, 2, 5, 5, 4, 5, 6, 3, 7, 6]~ \\ Charles R Greathouse IV, Feb 05 2018

def a(n): return sum([6, 2, 5, 5, 4, 5, 6, 3, 7, 6][int(d)] for d in str(n))
print([a(n) for n in range(77)]) # Michael S. Branicky, Jun 02 2021

a(n) = a(floor(n/10)) + a(n mod 10) for n > 9. - Reinhard Zumkeller, Mar 15 2013

a(n) = A010371(n) - A102679(n) + A102681(n) (subtract the number of digits 7 in n) = A277116(n) + A102683(n) (add number of digits 9 in n); and in particular, A063720(n) <= A277116(n) <= a(n) = A010371(n). - M. F. Hasler, Jun 17 2020

More terms from Matthew Conroy, Sep 13 2001

A010371 Number of segments used to represent n on a 7-segment calculator display; version where '6', '7' and '9' use 6, 4 and 6 segments, respectively.

Original entry on oeis.org

6, 2, 5, 5, 4, 5, 6, 4, 7, 6, 8, 4, 7, 7, 6, 7, 8, 6, 9, 8, 11, 7, 10, 10, 9, 10, 11, 9, 12, 11, 11, 7, 10, 10, 9, 10, 11, 9, 12, 11, 10, 6, 9, 9, 8, 9, 10, 8, 11, 10, 11, 7, 10, 10, 9, 10, 11, 9, 12, 11, 12, 8, 11, 11, 10, 11, 12, 10, 13, 12, 10, 6, 9, 9, 8, 9, 10, 8, 11, 10, 13, 9, 12, 12

Offset: 0

Olivier.Gagneux(AT)roche.com

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

			LCD Display (cf. Casio scientific calculator fx-3600P):
   _     _  _       _   _   _   _   _
  | | |  _| _| |_| |_  |_  | | |_| |_|
  |_| | |_  _|   |  _| |_|   | |_|  _|

R. Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for sequences related to calculator display

Segment variations: A006942, A063720, A074458, A277116.

Cf. A000120, A234691, A234692.

a010371 n = a010371_list !! n
a010371_list = [6,2,5,5,4,5,6,4,7,6] ++ f 10 where
   f x = (a010371 x' + a010371 d) : f (x + 1)
         where (x',d) = divMod x 10
-- Reinhard Zumkeller, Mar 15 2013

MapIndexed[(f[#2[[1]]-1] = #1)&, {6, 2, 5, 5, 4, 5, 6, 4, 7, 6}]; a[n_] := Total[f /@ IntegerDigits[n]]; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Mar 08 2017 *)

apply( {A010371(n)=digits(6255456476)[n%10+1]+if(n>9, self()(n\10))}, [0..99]) \\ M. F. Hasler, Jun 17 2020

For n > 9, a(n) = a(floor(n/10)) + a(n mod 10). - Reinhard Zumkeller, Aug 27 2008
a(n) = A000120(A234691(n)) = A000120(A234692(n))
  = A006942(n) + A102679(n) - A102681(n) (add number of digits 7)
= A074458(n) + A102683(n) (add number of digits 9). - M. F. Hasler, Jun 17 2020

Corrected and extended by Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 27 1999

Edited name, comments, cross-references. - M. F. Hasler, Jun 17 2020

A063720 Number of segments lit in a 7-segment display (as on a calculator) to represent the number n, variant 0: '6', '7' and '9' use 5, 3 and 5 segments, respectively.

Original entry on oeis.org

6, 2, 5, 5, 4, 5, 5, 3, 7, 5, 8, 4, 7, 7, 6, 7, 7, 5, 9, 7, 11, 7, 10, 10, 9, 10, 10, 8, 12, 10, 11, 7, 10, 10, 9, 10, 10, 8, 12, 10, 10, 6, 9, 9, 8, 9, 9, 7, 11, 9, 11, 7, 10, 10, 9, 10, 10, 8, 12, 10, 11, 7, 10, 10, 9, 10, 10, 8, 12, 10, 9, 5, 8, 8, 7, 8, 8, 6, 10, 8, 13, 9, 12, 12, 11, 12

Offset: 0

Deepan Majmudar (deepan.majmudar(AT)compaq.com), Aug 23 2001

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

			The number 8 on a digital readout (e.g., on a calculator display) can be represented as
   -
  | |
   -
  | |
   -
which uses all 7 segments. Therefore a(8) = 7.
From _M. F. Hasler_, Jun 17 2020: (Start)
This sequence uses the following representations:
       _       _   _       _       _   _   _
      | |   |  _|  _| |_| |_  |_    | |_| |_|
      |_|   | |_   _|   |  _| |_|   | |_|   |
.
See crossrefs for other variants. (End)

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
Index entries for sequences related to calculator display

For variants see A006942, A010371, A074458, A277116 (cf. comments).

Other related sequences: A018846, A018847, A018849, A038136, A053701.

a063720 n = a063720_list !! n
a063720_list = [6,2,5,5,4,5,5,3,7,5] ++ f 10 where
   f x = (a063720 x' + a063720 d) : f (x + 1)
         where (x',d) = divMod x 10
-- Reinhard Zumkeller, Mar 15 2013

a[n_ /; n <= 9] := a[n] = {6, 2, 5, 5, 4, 5, 5, 3, 7, 5}[[n+1]]; a[n_] := a[n] = a[Quotient[n, 10]] + a[Mod[n, 10]]; Table[a[n], {n, 0, 85}] (* Jean-François Alcover, Aug 12 2013, after Reinhard Zumkeller *)
Table[Total[IntegerDigits[n]/.{0->6,1->2,2->5,3->5,6->5,7->3,8->7,9->5}],{n,0,90}] (* Harvey P. Dale, Mar 27 2021 *)

apply( {A063720(n)=digits(6255455375)[n%10+1]+if(n>9, self()(n\10))}, [0..99]) \\ M. F. Hasler, Jun 17 2020

a(n) = a(floor(n/10)) + a(n mod 10) for n > 9. - Reinhard Zumkeller, Mar 15 2013

a(n) <= A277116(n) <= min{A006942(n), A074458(n)} <= A010371(n); differences between these are given, e.g., by A102677(n) - A102679(n) (= number of digits 7 in n). - M. F. Hasler, Jun 17 2020

More terms from Matthew Conroy, Sep 13 2001

Definition clarified by M. F. Hasler, Jun 17 2020

A074458 Number of segments lit to display the number n on a 7-segment display (as in pocket calculators): variant where '6', '7' and '9' use 6, 4 resp. 5 segments.

Original entry on oeis.org

6, 2, 5, 5, 4, 5, 6, 4, 7, 5, 8, 4, 7, 7, 6, 7, 8, 6, 9, 7, 11, 7, 10, 10, 9, 10, 11, 9, 12, 10, 11, 7, 10, 10, 9, 10, 11, 9, 12, 10, 10, 6, 9, 9, 8, 9, 10, 8, 11, 9, 11, 7, 10, 10, 9, 10, 11, 9, 12, 10, 12, 8, 11, 11, 10, 11, 12, 10, 13, 11, 10, 6, 9, 9, 8, 9, 10, 8, 11

Offset: 0

Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 22 2002

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

			LED display:
   _       _   _       _   _   _   _   _
  | |   |  _|  _| |_| |_  |_  | | |_| |_|
  |_|   | |_   _|   |  _| |_|   | |_|   |
.
so we have a(0) = 6, a(1) = 2, a(2) = 5 ...

Index entries for sequences related to calculator display

Cf. A074459.
For other versions of this sequence, see A006942 (7 with one segment less), A063720 (6 and 7 with one segment less), A010371 (9 with one segment more), A277116 (7 with one segment less, 9 with one segment more).
Cf. A234691, A234692, A000120.

apply( {A074458(n)=digits(6255456475)[n%10+1]+if(n>9,self()(n\10))}, [0..99]) \\ M. F. Hasler, Jun 17 2020

From M. F. Hasler, Jun 17 2020: (Start)
a(n) = a(n mod 10) + a(floor(n/10)) for n > 9.
a(n) = A006942(n) - A102679(n) + A102681(n). (End)

Example edited by Jon E. Schoenfield, Jul 30 2017

Edited and extended to n > 9 by M. F. Hasler, Jun 17 2020

A277116 Number of segments used to represent the number n on a 7-segment display: variant where digits 6, 7 and 9 use 6, 3 and 5 segments, respectively.

Original entry on oeis.org

6, 2, 5, 5, 4, 5, 6, 3, 7, 5, 8, 4, 7, 7, 6, 7, 8, 5, 9, 7, 11, 7, 10, 10, 9, 10, 11, 8, 12, 10, 11, 7, 10, 10, 9, 10, 11, 8, 12, 10, 10, 6, 9, 9, 8, 9, 10, 7, 11, 9, 11, 7, 10, 10, 9, 10, 11, 8, 12, 10, 12, 8, 11, 11, 10, 11, 12, 9, 13, 11, 9, 5, 8, 8, 7, 8, 9

Offset: 0

Eric Ginsburg, Sep 30 2016

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

			For n = 29, digit '2' uses 5 segments and digit '9' uses 5 segments. So, a(29) = 10. - _Indranil Ghosh_, Feb 02 2017
The digits are represented as follows:
   _     _  _       _   _   _   _   _
  | | |  _| _| |_| |_  |_    | |_| |_|
  |_| | |_  _|   |  _| |_|   | |_|   | . - _M. F. Hasler_, Jun 17 2020

Indranil Ghosh, Table of n, a(n) for n = 0..50000
Wikipedia, Seven-segment display.
Index entries for sequences related to calculator display

Segment variations: A006942, A010371, A063720, A074458.

Cf. A102683, A234691, A234692.

Table[Total[IntegerDigits[n] /. {0 -> 6, 1 -> 2, 2 -> 5, 3 -> 5, 6 -> 6, 7 -> 3, 8 -> 7, 9 -> 5}], {n, 0, 120}] (* Michael De Vlieger, Sep 30 2016 *)

a(n) = my(segm=[6, 2, 5, 5, 4, 5, 6, 3, 7, 5], d=digits(n), s=0); if(n==0, s=6, for(k=1, #d, s=s+segm[d[k]+1])); s \\ Felix Fröhlich, Oct 05 2016

def A277116(n):
    s=0
    for i in str(n):
        s+=[6,2,5,5,4,5,6,3,7,5][int(i)]
    return s # Indranil Ghosh, Feb 02 2017

a(n) = A006942(n) - A102683(n). - Omar E. Pol, Sep 30 2016
a(n) = A063720(n) + A102677(n) - A102679(n) (add number of digits 6)
  = A074458(n) - A102679(n) + A102681(n) (subtract number of digits 7)
  and thus A063720(n) <= a(n) <= min(A074458(n), A006942(n)) <= A010371(n). - M. F. Hasler, Jun 17 2020

Better definition and more terms from Omar E. Pol, Sep 30 2016

Edited by M. F. Hasler, Jun 17 2020

A102680 Number of digits >= 7 in the decimal representations of all integers from 0 to n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 3, 3, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 6, 6, 6, 6, 7, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 17, 18, 18, 18, 18, 18, 18, 18, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30, 32, 34, 35, 36

Offset: 0

N. J. A. Sloane, Feb 03 2005

The total number of digits >= 7 occurring in all the numbers 0, 1, 2, ..., n (in decimal representation). - Hieronymus Fischer, Jun 10 2012

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Partial sums of A102679.
Cf. A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums of A102669.
Cf. A000120, A000788, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=7 then ct:=ct+1 else ct:=ct fi od: ct: end:
seq(add(p(i),i=0..n), n=0..90);
# Emeric Deutsch

Accumulate[Table[Count[IntegerDigits[n],?(#>6&)],{n,0,90}]] (* _Harvey P. Dale, Sep 04 2018 *)

From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = (1/2)*Sum_{j=1..m+1} (floor(n/10^j + 7/10)*(2n + 2 - (2/5 + floor(n/10^j + 7/10))*10^j) - floor(n/10^j)*(2n + 2 - (1+floor(n/10^j)) * 10^j)), where m=floor(log_10(n)).
a(n) = (n+1)*A102679(n) + (1/2)*Sum_{j=1..m+1} (((-2/5)*floor(n/10^j + 7/10) + floor(n/10^j))*10^j - (floor(n/10^j + 7/10)^2 - floor(n/10^j)^2)*10^j), where m=floor(log_10(n)).
a(10^m-1) = 3*m*10^(m-1).
(this is total number of digits >= 7 occurring in all the numbers with <= m places).
G.f.: g(x) = (1/(1-x)^2)*Sum_{j>=0} (x^(7*10^j) - x^(10*10^j))/(1-x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 23 2005

cp's OEIS Frontend

A006942 Number of segments used to represent n on calculator display, variant 5: digits '6', '7' and '9' use 6, 3 and 6 segments, respectively.

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A010371 Number of segments used to represent n on a 7-segment calculator display; version where '6', '7' and '9' use 6, 4 and 6 segments, respectively.

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A063720 Number of segments lit in a 7-segment display (as on a calculator) to represent the number n, variant 0: '6', '7' and '9' use 5, 3 and 5 segments, respectively.

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A074458 Number of segments lit to display the number n on a 7-segment display (as in pocket calculators): variant where '6', '7' and '9' use 6, 4 resp. 5 segments.

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A277116 Number of segments used to represent the number n on a 7-segment display: variant where digits 6, 7 and 9 use 6, 3 and 5 segments, respectively.

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A102680 Number of digits >= 7 in the decimal representations of all integers from 0 to n.

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