A018846 -id:A018846

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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.

+10
19

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

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

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to calculator display

FORMULA

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

EXAMPLE

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)

MATHEMATICA

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 *)

PROG

(Haskell)

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

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

CROSSREFS

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

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

KEYWORD

nonn,base,nice

AUTHOR

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

EXTENSIONS

More terms from Matthew Conroy, Sep 13 2001

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

STATUS

approved

A053701

Vertically symmetric numbers.

+10
12

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Numbers that are symmetric about a vertical mirror.

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

LINKS

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

MAPLE

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

PROG

(Python)

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

CROSSREFS

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

KEYWORD

nonn,base

AUTHOR

Henry Bottomley, Feb 14 2000

EXTENSIONS

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

STATUS

approved

A018847

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

+10
7

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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

LINKS

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

MATHEMATICA

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 *)

PROG

(PARI) {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

(PARI) 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

(Python)

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

CROSSREFS

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

KEYWORD

nonn,base

AUTHOR

David W. Wilson

STATUS

approved

A018849

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

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..20.

PROG

(PARI) 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

KEYWORD

nonn,base

AUTHOR

David W. Wilson

STATUS

approved

A115045

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

+10
0

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..34.

CROSSREFS

Cf. A018846.

KEYWORD

fini,full,nonn,base

AUTHOR

Lekraj Beedassy, Feb 28 2006

STATUS

approved

A133030

Divisors of 5130.

+10
0

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

LINKS

Table of n, a(n) for n=1..32.

Index entries for sequences related to divisors of numbers

MATHEMATICA

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

PROG

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

CROSSREFS

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

KEYWORD

fini,full,nonn,easy

AUTHOR

Omar E. Pol, Oct 27 2007

STATUS

approved

A321310

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

+10
0

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

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

LINKS

Table of n, a(n) for n=0..61.

EXAMPLE

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.

MATHEMATICA

{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 *)

CROSSREFS

Cf. A018846, A053701, A080228.

KEYWORD

nonn,base,tabf

AUTHOR

Kritsada Moomuang, Nov 03 2018

STATUS

approved

A321702

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

+10
0

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

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

LINKS

Table of n, a(n) for n=1..60.

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

FORMULA

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

EXAMPLE

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.

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A000787, A007284, A018846.

KEYWORD

nonn,base

AUTHOR

Kritsada Moomuang, Nov 17 2018

STATUS

approved

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