A053701 -id:A053701 - cp's OEIS frontend

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.

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

A106605 Vertically symmetrical dates DDMMYYYY excluding years which are divisible by 10, considered as numbers, in increasing order.

Original entry on oeis.org

10011001, 10025001, 10052001, 10088001, 10100101, 10111101, 10125101, 11011011, 11025011, 11052011, 11088011, 11100111, 11111111, 11125111, 12011051, 12025051, 12052051, 12088051, 12100151, 12111151, 12125151, 15011021, 15025021, 15052021

Offset: 1

Nicolas Graner, Eric Angelini and Alexandre Wajnberg, May 10 2005

2 and 5 are taken as mirror images (as on calculator displays). a(1)=10011001, a(13)=11111111 and a(38)=20052005 (May 20 2005!) also share the unique property of having two symmetrical halves.

This sequence has exactly 70 terms, ending with 28125185 (Dec 28 5185).

Nathaniel Johnston, Table of n, a(n) for n = 1..70 (full sequence)

Cf. A053701.

compdig := proc(n) if(n=2)then return 5: elif(n=5)then return 2: elif(n=0 or n=1 or n=8)then return n: else return -1: fi: end: for d from 10 to 28 do for m from 1 to 12 do for y from 1 to 8888 do dt:=1000000*d+10000*m+y: dig:=convert(dt,base,10): if(dig[1]=compdig(dig[8]) and dig[2]=compdig(dig[7]) and dig[3]=compdig(dig[6]) and dig[4]=compdig(dig[5]))then print(dt): fi: od: od: od: # Nathaniel Johnston, May 17 2011

Definition clarified by Hieronymus Fischer, Apr 01 2012

A107273 Vertically symmetrical dates MMDDYYYY (American notation) excluding years which are divisible by 10, considered as numbers, in increasing order.

Original entry on oeis.org

10011001, 10025001, 10052001, 10088001, 10100101, 10111101, 10125101, 10152101, 10188101, 10200501, 10211501, 10225501, 10252501, 10288501, 11011011, 11025011, 11052011, 11088011, 11100111, 11111111, 11125111

Offset: 1

Alexandre Wajnberg, May 19 2005

2 and 5 are taken as mirror images (as on calculator displays). a(1)=10011001 and a(20)=11111111 shared the property to present also two symmetrical halves.

This sequence has exactly 42 terms, ending with 12288551 (Dec. 28th 8551).

Iain Fox, Table of n, a(n) for n = 1..42

Condensed American notation dates: A107274.
Metric convention dates: A107275.
Condensed European notation dates: A107276.
Cf. A053701, A106605.

a(n) = my(d=digits(126+25*((n-1)\14)+(n-1)%14, 5)); fromdigits(apply(i->[0, 1, 2, 5, 8, 5, 2][i+1], concat(d, apply(i->i+3*bitand(i, 2)/2, Vecrev(d))))) \\ Iain Fox, Jul 08 2022

Definition clarified by Hieronymus Fischer, Apr 01 2012

A107275 Vertically symmetrical dates YYYYMMDD (metric convention) for years >=1000, considered as numbers, in increasing order which here is also the chronological order.

Original entry on oeis.org

10011001, 10100101, 10111101, 10200501, 10500201, 10511201, 10800801, 11011011, 11100111, 11111111, 11200511, 11500211, 11511211, 11800811, 15011021, 15100121, 15111121, 15200521, 15500221, 15511221, 15800821

Offset: 1

Alexandre Wajnberg, May 19 2005

A little over 30 years ago, almost all nations agreed (...) on the (adoption and) use of the "metric system". For example, April 7, 1975, is expressed as 1975 04 07 (R. K. Guy)

This sequence has exactly 84 terms, ending with 85800828 (8580 August 28th).

			2 and 5 are taken as mirror images (as on calculator displays). a(1)=10011001 and a(10)=11111111 shared the property to present also two symmetrical halves.

Cf. A053701, A106605.

Definition clarified by Hieronymus Fischer, Apr 01 2012

A018846 Strobogrammatic numbers: numbers that are the same upside down (using calculator-style numerals).

Original entry on oeis.org

0, 1, 2, 5, 8, 11, 22, 55, 69, 88, 96, 101, 111, 121, 151, 181, 202, 212, 222, 252, 282, 505, 515, 525, 555, 585, 609, 619, 629, 659, 689, 808, 818, 828, 858, 888, 906, 916, 926, 956, 986, 1001, 1111, 1221, 1551, 1691, 1881, 1961, 2002, 2112, 2222, 2552, 2692, 2882

Offset: 1

David W. Wilson

A018847 lists primes in this sequence. - M. F. Hasler, May 05 2012

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Cf. A053701 (vertically symmetric numbers), A048708.

is_A018846(n,t=Vec("012..59.86"))={ apply(x->t[eval(x)+1], n=Vec(Str(n)))==vecextract(n, "-1..1") } \\ M. F. Hasler, May 05 2012

from itertools import count, islice, product
def ud(s): return s[::-1].translate({ord('6'):ord('9'), ord('9'):ord('6')})
def A018846gen(): # generator of terms
    yield from [0, 1, 2, 5, 8]
    for d in count(2):
        for first in "125689":
            for rest in product("0125689", repeat=d//2-1):
                left = first + "".join(rest)
                for mid in [[""], ["0", "1", "2", "5", "8"]][d%2]:
                    yield int(left + mid + ud(left))
print(list(islice(A018846gen(), 54))) # Michael S. Branicky, Jul 09 2022

A332118 a(n) = (10^(2n+1) - 1)/9 + 7*10^n.

Original entry on oeis.org

8, 181, 11811, 1118111, 111181111, 11111811111, 1111118111111, 111111181111111, 11111111811111111, 1111111118111111111, 111111111181111111111, 11111111111811111111111, 1111111111118111111111111, 111111111111181111111111111, 11111111111111811111111111111, 1111111111111118111111111111111

Offset: 0

M. F. Hasler, Feb 09 2020

See A107648 = {1, 4, 6, 7, 384, 666, ...} for the indices of primes.

Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).
Patrick De Geest, Palindromic Wing Primes: (1)8(1), updated: June 25, 2017.
Makoto Kamada, Factorization of 11...11811...11, updated Dec 11 2018.
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Cf. (A077791-1)/2 = A107648: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes), A077798 (palindromic wing primes), A088281 (primes 1..1x1..1), A068160 (smallest of given length), A053701 (vertically symmetric numbers).
Cf. A332128 .. A332178, A181965 (variants with different repeated digit 2, ..., 9).
Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).

A332118 := n -> (10^(2*n+1)-1)/9+7*10^n;

Array[(10^(2 # + 1)-1)/9 + 7*10^# &, 15, 0]

apply( {A332118(n)=10^(n*2+1)\9+7*10^n}, [0..15])

def A332118(n): return 10**(n*2+1)//9+7*10**n

a(n) = A138148(n) + 8*10^n = A002275(2n+1) + 7*10^n.
G.f.: (8 - 707*x + 600*x^2)/((1 - x)(1 - 10*x)(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

A080228 Numbers containing the digits 0, 1, 2, 5 or 8 only.

Original entry on oeis.org

0, 1, 2, 5, 8, 10, 11, 12, 15, 18, 20, 21, 22, 25, 28, 50, 51, 52, 55, 58, 80, 81, 82, 85, 88, 100, 101, 102, 105, 108, 110, 111, 112, 115, 118, 120, 121, 122, 125, 128, 150, 151, 152, 155, 158, 180, 181, 182, 185, 188, 200, 201, 202, 205, 208, 210, 211, 212, 215

Offset: 1

Giannopoulos P. (pgiannop1(AT)yahoo.com), Mar 17 2003

Numbers that are still numbers when viewed in a mirror, writing 2 and 5 as in calculator displays.

P. Giannopoulos, The Brainteasers, unpublished

Harvey P. Dale, Table of n, a(n) for n = 1..3000

Cf. A080792, A053701.

FromDigits/@Tuples[{0,1,2,5,8},3] (* Harvey P. Dale, Sep 10 2017 *)

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

Offset corrected by Arkadiusz Wesolowski, Sep 23 2011

A080792 Numbers which when seen in a mirror are different numbers.

Original entry on oeis.org

2, 5, 10, 12, 15, 18, 20, 21, 22, 28, 50, 51, 55, 58, 80, 81, 82, 85, 100, 102, 105, 108, 110, 115, 118, 120, 121, 125, 150, 151, 152, 158, 180, 182, 185, 200, 202, 208, 210, 212, 218, 220, 221, 225, 228, 250, 252, 258, 280, 282, 288, 500, 505

Offset: 1

P. Giannopoulos (pgiannop1(AT)yahoo.com), Mar 13 2003

P. Giannopoulos, The Brainteasers, unpublished.

Cf. A053701, A080228.

A107276 Vertically symmetrical dates DDMMYY ("condensed European notation") considered as numbers, in increasing order.

Original entry on oeis.org

101101, 111111, 121151, 151121, 181181, 201105, 211115, 221155, 251125, 281185

Offset: 1

Alexandre Wajnberg, May 19 2005

2 and 5 are taken as mirror images (as on calculator displays). From now on, the next symmetric date is November 20 2005 (201105). a(1)=101101, a(2)=111111 and a(5)=181181 share the property to present also two symmetrical halves. Next one is November 11 2011 (11 11 11).

Next one is Nov 21 2015 (211115). - M. F. Hasler, Feb 27 2013

Cf. A053701, A106605.

A107276(n)=101101+[8008,0,1001,2005,5002][n%5+1]*10+n\6*100004 \\ M. F. Hasler, Feb 28 2013

Edited by Jon E. Schoenfield, Feb 10 2015

A107274 Vertically symmetrical dates MMDDYY ("condensed American notation") considered as numbers, in increasing order.

Original entry on oeis.org

101101, 102501, 111111, 112511, 121151, 122551

Offset: 1

Alexandre Wajnberg, May 19 2005

2 and 5 are taken as mirror images (as on calculator displays). a(1)=101101 and a(3)=111111, share the property to present also two symmetrical halves. From now on, the next one is Nov 11th 11.

Cf. A053701, A106605.

cp's OEIS Frontend

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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A106605 Vertically symmetrical dates DDMMYYYY excluding years which are divisible by 10, considered as numbers, in increasing order.

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A107273 Vertically symmetrical dates MMDDYYYY (American notation) excluding years which are divisible by 10, considered as numbers, in increasing order.

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A107275 Vertically symmetrical dates YYYYMMDD (metric convention) for years >=1000, considered as numbers, in increasing order which here is also the chronological order.

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A018846 Strobogrammatic numbers: numbers that are the same upside down (using calculator-style numerals).

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A332118 a(n) = (10^(2n+1) - 1)/9 + 7*10^n.

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A080228 Numbers containing the digits 0, 1, 2, 5 or 8 only.

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A080792 Numbers which when seen in a mirror are different numbers.

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