A018846 -id:A018846 - 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

A053701 Vertically symmetric numbers.

Original entry on oeis.org

0, 1, 8, 11, 25, 52, 88, 101, 111, 181, 205, 215, 285, 502, 512, 582, 808, 818, 888, 1001, 1111, 1251, 1521, 1881, 2005, 2115, 2255, 2525, 2885, 5002, 5112, 5252, 5522, 5882, 8008, 8118, 8258, 8528, 8888, 10001, 10101, 10801, 11011, 11111, 11811

Offset: 1

Henry Bottomley, Feb 14 2000

Numbers that are symmetric about a vertical mirror.

2 and 5 are taken as mirror images (as on calculator displays).

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..2500 from Nathaniel Johnston)

Cf. A000787, A007284, A018846 (strobogrammatic numbers).

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: isA053701 := proc(n) local d,l,j: d:=convert(n,base,10): l:=nops(d): for j from 1 to ceil(l/2) do if(not d[j]=compdig(d[l-j+1]))then return false: fi: od: return true: end: for n from 0 to 10000 do if(isA053701(n))then printf("%d, ",n): fi: od: # Nathaniel Johnston, May 17 2011

from itertools import count, islice, product
def lr(s): return s[::-1].translate({ord('2'):ord('5'), ord('5'):ord('2')})
def A053701gen(): # generator of terms
    yield from [0, 1, 8]
    for d in count(2):
        for first in "1258":
            for rest in product("01258", repeat=d//2-1):
                left = first + "".join(rest)
                for mid in [[""], ["0", "1", "8"]][d%2]:
                    yield int(left + mid + lr(left))
print(list(islice(A053701gen(), 45))) # Michael S. Branicky, Jul 09 2022

More terms from Larry Reeves (larryr(AT)acm.org), Oct 01 2001

A018847 Strobogrammatic primes: the same upside down (calculator-style numerals).

Original entry on oeis.org

2, 5, 11, 101, 151, 181, 619, 659, 6229, 10501, 12821, 15551, 16091, 18181, 19861, 60209, 60509, 61519, 61819, 62129, 116911, 119611, 160091, 169691, 191161, 196961, 605509, 620029, 625529, 626929, 650059, 655559, 656959, 682289, 686989, 688889

Offset: 1

David W. Wilson

This is the subsequence of primes in A018846. - M. F. Hasler, May 05 2012

Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..648 from M. F. Hasler)

Cf. A007597 (more restrictive version not allowing digits 2 or 5).

lst = {}; fQ[n_] := Block[{allset = {0, 1, 2, 5, 6, 8, 9}, id = IntegerDigits@n}, Union@ Join[id, allset] == allset && Reverse[id /. {6 -> 9, 9 -> 6}] == id]; Do[ If[ PrimeQ@n && fQ@n, AppendTo[lst, n]], {n, 700000}]; lst (* Robert G. Wilson v, Feb 27 2007 *)

{write("/tmp/b018847.txt","1 2\n2 5"); c=2; s2=[0,1,2,5,6,8,9]; s=[0,1,2,5,8]; s1=[0,1,2,5,9,8,6]; for(n=2,9, p1=vector( (n+1)\2, i, 10^(i-1)); p2=vector( (n+1)\2, i, 10^(n-i)); forvec( v=vector((n+1)\2,i,if( i>1, [ 1,if( i>n\2, #s, #s1)], [2,5])), v[1]==3 & v[1]=5; ispseudoprime( t=sum(i=1,n\2,p1[i]*s1[v[i]]+p2[i]*s2[v[i]] ) +if(n%2,p1[#p1]*s[v[#v]] )) & /* print1(t",") */ write("/tmp/b018847.txt",c++" "t)))} \\ - M. F. Hasler, Apr 26 2012

is_A018847(n,t=Vec("012..59.86"))={ isprime(n) & 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
from sympy import isprime
def A018847_gen(): # generator of terms
    r, t, u = ''.maketrans('69','96'), set('0125689'), {0,1,2,5,8}
    for x in count(1):
        for y in range(10**(x-1),10**x):
            if y%10 in u:
                s = str(y)
                if set(s) <= t and isprime(m:=int(s+s[-2::-1].translate(r))):
                    yield m
        for y in range(10**(x-1),10**x):
            s = str(y)
            if set(s) <= t and isprime(m:=int(s+s[::-1].translate(r))):
                yield m
A018847_list = list(islice(A018847_gen(),20)) # Chai Wah Wu, Apr 09 2024

A018849 Strobogrammatic squares: the same upside down (calculator-style numerals).

Original entry on oeis.org

0, 1, 121, 6889, 10201, 69169, 1002001, 5221225, 100020001, 109181601, 522808225, 602555209, 10000200001, 62188888129, 1000002000001, 1212225222121, 100000020000001, 10000000200000001, 10022212521222001, 12102202520220121

Offset: 1

David W. Wilson

Subsequence of squares in A018846. - Michel Marcus, Aug 04 2014

is_A018846(n, t=Vec("012..59.86"))={ apply(x->t[eval(x)+1], n=Vec(Str(n)))==vecextract(n, "-1..1"); }
lista(nn) = {for(n=0, nn, if (is_A018846(n^2), print1(n^2, ", ")));} \\ Michel Marcus, Aug 04 2014

A115045 Strobogrammatic time display in hours and minutes on a 24-hour four spaced digital clock. Leading zeros omitted.

Original entry on oeis.org

0, 10, 20, 50, 101, 111, 121, 151, 202, 212, 222, 252, 505, 515, 525, 555, 609, 619, 629, 659, 808, 818, 858, 906, 916, 926, 956, 1001, 1111, 1221, 1551, 2002, 2112, 2222

Offset: 1

Lekraj Beedassy, Feb 28 2006

050 and 2112 for instance stand for 0:50 and 21:12, i.e. 0h50mn and 21h12mn respectively.

Cf. A018846.

A133030 Divisors of 5130.

Original entry on oeis.org

1, 2, 3, 5, 6, 9, 10, 15, 18, 19, 27, 30, 38, 45, 54, 57, 90, 95, 114, 135, 171, 190, 270, 285, 342, 513, 570, 855, 1026, 1710, 2565, 5130

Offset: 1

Omar E. Pol, Oct 27 2007

5130 spells OEIS when turned upside down on a calculator: 57*90 = 5130 ---> OEIS.

Index entries for sequences related to divisors of numbers

Cf. A000787, A001840, A007597, A018278, A018365, A018846, A048889, A080789.

Divisors[5130] (* Paolo Xausa, Aug 10 2024 *)

divisors(5130) \\ Charles R Greathouse IV, Sep 06 2016

A321310 List of pairs of numbers with mirror symmetry (calculator-style numerals).

Original entry on oeis.org

0, 0, 1, 1, 2, 5, 5, 2, 8, 8, 11, 11, 12, 51, 15, 21, 18, 81, 21, 15, 22, 55, 25, 25, 28, 85, 51, 12, 52, 52, 55, 22, 58, 82, 81, 18, 82, 58, 85, 28, 88, 88, 101, 101, 102, 501, 105, 201, 108, 801, 111, 111, 112, 511, 115, 211, 118, 811, 121, 151, 122, 551

Offset: 0

Kritsada Moomuang, Nov 03 2018

2 and 5 are taken as mirror images (as on calculator displays).

			The sequence begins:
   0,  0;
   1,  1;
   2,  5;
   5,  2;
   8,  8;
  11, 11;
  12, 51;
  15, 21;
  18, 81;
  21, 15;
  22, 55;
  25, 25;
  28, 85;
...
81 has its reflection as 18 in a mirror.
125 has its reflection as 251 in a mirror.

Cf. A018846, A053701, A080228.

{0, 0}~Join~Array[If[Mod[#, 10] == 0, Nothing, If[IntegerLength[#1] == Length[#2], {#1, FromDigits@ #2}, Nothing] & @@ {#, Reverse@ IntegerDigits@ # /. {2 -> 5, 3 -> Nothing, 4 -> Nothing, 5 -> 2, 6 -> Nothing, 7 -> Nothing, 9 -> Nothing}}] &, 123] // Flatten (* Michael De Vlieger, Nov 05 2018 *)

A321702 Numbers that are still valid after a horizontal reflection on a calculator display.

Original entry on oeis.org

0, 1, 2, 3, 5, 8, 10, 11, 12, 13, 15, 18, 20, 21, 22, 23, 25, 28, 30, 31, 32, 33, 35, 38, 50, 51, 52, 53, 55, 58, 80, 81, 82, 83, 85, 88, 100, 101, 102, 103, 105, 108, 110, 111, 112, 113, 115, 118, 120, 121, 122, 123, 125, 128, 130, 131, 132, 133, 135, 138

Offset: 1

Kritsada Moomuang, Nov 17 2018

Note that these numbers may not be unchanged after a horizontal reflection.
2 and 5 are taken as mirror images (as on calculator displays).
A007284 is a subsequence.
Also, numbers whose all digits are Fibonacci numbers. - Amiram Eldar, Feb 15 2024

			The sequence begins:
0, 1, 2, 3, 5, 8, 10, 11, 12, 13, ...;
0, 1, 5, 3, 2, 8, 10, 11, 15, 13, ...;
23 has its reflection as 53 in a horizontal mirror.
182 has its reflection as 185 in a horizontal mirror.

Robert Baillie and Thomas Schmelzer, Summing Kempner's Curious (Slowly-Convergent) Series, Mathematica Notebook kempnerSums.nb, Wolfram Library Archive, 2008.

Cf. A000787, A007284, A018846.

Select[Range[0, 140], Intersection[IntegerDigits[#], {4, 6, 7, 9}] == {} &] (* Amiram Eldar, Nov 17 2018 *)

a(n, d=[0, 1, 2, 3, 5, 8]) = fromdigits(apply(k -> d[1+k], digits(n-1, #d))) \\ Rémy Sigrist, Nov 17 2018

Sum_{n>=2} 1/a(n) = 4.887249145579262560308470922947674796541485176473171687107616547235128170930... (calculated using Baillie and Schmelzer's kempnerSums.nb, see Links). - Amiram Eldar, Feb 15 2024

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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A053701 Vertically symmetric numbers.

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A018847 Strobogrammatic primes: the same upside down (calculator-style numerals).

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PARI

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A018849 Strobogrammatic squares: the same upside down (calculator-style numerals).

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PARI

A115045 Strobogrammatic time display in hours and minutes on a 24-hour four spaced digital clock. Leading zeros omitted.

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A133030 Divisors of 5130.

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Mathematica

PARI

A321310 List of pairs of numbers with mirror symmetry (calculator-style numerals).

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Mathematica

A321702 Numbers that are still valid after a horizontal reflection on a calculator display.

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Mathematica