cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

A079401 Partial sums of A079399.

Original entry on oeis.org

3, 4, 6, 8, 11, 13, 16, 20, 23, 25, 29, 31, 34, 37, 41, 44, 48, 53, 57, 60, 65, 68, 72, 76, 81, 85, 90, 96, 101, 105, 110, 113, 117, 121, 126, 130, 135, 141, 146, 150, 156, 160, 165, 170, 176, 181, 187, 194, 200, 205, 210, 213, 217, 221, 226, 230, 235, 241, 246, 250
Offset: 0

Views

Author

Jon Perry, Feb 16 2003

Keywords

Examples

			a(3) = 3+1+2 = 6.

Crossrefs

Cf. A079399.

Programs

  • Mathematica
    Accumulate[With[{br=Thread[Range[0,9]->{3,1,2,2,3,2,3,4,3,2}]}, Total/@ Table[ IntegerDigits[n]/.br,{n,0,100}]]] (* Harvey P. Dale, Aug 08 2016 *)
  • PARI
    { braille=[3,1,2,2,3,2,3,4,3,2]; bs=0; for (n=0,99, b=braille[n%10+1]; if (n>9,b=b+braille[n\10+1]); bs=bs+b; print1(bs",")) }

Extensions

Offset corrected by Sean A. Irvine, Aug 12 2025

A072283 Number of raised dots to represent n in Braille.

Original entry on oeis.org

7, 5, 6, 6, 7, 6, 7, 8, 7, 6, 8, 6, 7, 7, 8, 7, 8, 9, 8, 7, 9, 7, 8, 8, 9, 8, 9, 10, 9, 8, 9, 7, 8, 8, 9, 8, 9, 10, 9, 8, 10, 8, 9, 9, 10, 9, 10, 11, 10, 9, 9, 7, 8, 8, 9, 8, 9, 10, 9, 8, 10, 8, 9, 9, 10, 9, 10, 11, 10, 9, 11, 9, 10, 10, 11, 10, 11, 12, 11, 10, 10, 8, 9, 9, 10, 9, 10, 11, 10, 9
Offset: 0

Views

Author

Rick L. Shepherd, Jul 10 2002

Keywords

Comments

Each term of this sequence includes 4, the number of raised dots to represent the numeral sign. This is normally necessary since the representations of the numerals "1" through "9" and then "0" are otherwise identical to the representations of the letters "a" through "j", respectively. In some contexts the numeral sign is unnecessary.

Examples

			a(10) = 8 because "10" is represented by the numeral sign "#" (4 raised dots), the digit one (1 raised dot) and digit zero (3 raised dots) and 4 + 3 + 1 = 8. Here is a depiction of the Braille representation, where "o" denotes a raised dot, "-" denotes unused space and each Braille character occupies a 3 X 2 cell:
-o o- -o
-o -- oo
oo -- --

Links

Crossrefs

Equals A079399(n) + 4.

Programs

  • Python
    B=[3,1,2,2,3,2,3,4,3,2]
def A072283(n):
    s=0
    for i in str(n):
        s+=B[int(i)]
    return s+4 # Indranil Ghosh, Jan 13 2017

Formula

The decimal digits map to numbers of Braille raised dots as follows: 0 -> 3, 1 -> 1, 2 -> 2, 3 -> 2, 4 -> 3, 5 -> 2, 6 -> 3, 7 -> 4, 8 -> 3 and 9 -> 2.

A121018 Value of n written in Braille, seen as 3 X 2 bit-code: 1 for a raised dot and 0 for an empty dot position.

Original entry on oeis.org

28, 32, 40, 48, 52, 36, 56, 60, 44, 24, 2076, 2080, 2088, 2096, 2100, 2084, 2104, 2108, 2092, 2072, 2588, 2592, 2600, 2608, 2612, 2596, 2616, 2620, 2604, 2584, 3100, 3104, 3112, 3120, 3124, 3108, 3128, 3132, 3116, 3096, 3356, 3360, 3368, 3376, 3380, 3364
Offset: 0

Views

Author

Reinhard Zumkeller, Jul 23 2006

Keywords

Comments

A000120(a(n)) = A079399(n).

Examples

			...... +-----+
n=0: . | _ . | -> (01)(11)(00)
...... | . . | .. -> 011100[bin] = 28 = a(0)
...... | _ _ |
...... +-----+
n=1: . | . _ | -> (10)(00)(00)
...... | _ _ | .. -> 100000[bin] = 32 = a(1)
...... | _ _ |
...... +-----+
n=2: . | . _ | -> (10)(10)(00)
...... | . _ | .. -> 101000[bin] = 40 = a(2)
...... | _ _ |
...... +-----+
n=3: . | . . | -> (11)(00)(00)
...... | _ _ | .. -> 110000[bin] = 48 = a(3)
...... | _ _ |
...... +-----+
n=4: . | . . | -> (11)(01)(00)
...... | _ . | .. -> 110100[bin] = 52 = a(4)
...... | _ _ |
...... +-----+
n=5: . | . _ | -> (10)(01)(00)
...... | _ . |.. -> 100100[bin] = 36 = a(5)
...... | _ _ |
...... +-----+
n=6: . | . . | -> (11)(10)(00)
...... | . _ | .. -> 111000[bin] = 56 = a(6)
...... | _ _ |
...... +-----+
n=7: . | . . | -> (11)(11)(00)
...... | . . | .. -> 111100[bin] = 60 = a(7)
...... | _ _ |
...... +-----+
n=8: . | . _ | -> (10)(11)(00)
...... | . . | .. -> 101100[bin] = 44 = a(8)
...... | _ _ |
...... +-----+
n=9: . | _ . | -> (01)(10)(00)
...... | . _ | .. -> 011000[bin] = 24 = a(9)
...... | _ _ |
...... +-----+.

Links

Crossrefs

Cf. A121019.

Programs

  • Mathematica
    a[0]=28;a[1]= 32;a[2]= 40;a[3]= 48;a[4]= 52;a[5]= 36;a[6]= 56;a[7]= 60;a[8]= 44;a[9]= 24;a[n_]:=a[Floor[n/10]]*64+a[Mod[n,10]];Table[a[n],{n,0,45}] (* James C. McMahon, Oct 11 2024 *)

Formula

a(n) = a(floor(n/10))*64 + a(n mod 10) for n>9.

A121019 Value of n written in Braille, seen as 2 X 3 bit-code: 1 for a raised dot and 0 for an empty dot position.

Original entry on oeis.org

22, 32, 48, 36, 38, 34, 52, 54, 50, 20, 2070, 2080, 2096, 2084, 2086, 2082, 2100, 2102, 2098, 2068, 3094, 3104, 3120, 3108, 3110, 3106, 3124, 3126, 3122, 3092, 2326, 2336, 2352, 2340, 2342, 2338, 2356, 2358, 2354, 2324, 2454, 2464, 2480, 2468, 2470, 2466
Offset: 0

Views

Author

Reinhard Zumkeller, Jul 23 2006

Keywords

Comments

A000120(a(n)) = A079399(n).

Examples

			...... +-----+
n=0: . | _ . | -> (010)(110)
...... | . . | .. -> 010110[bin] = 22 = a(0)
...... | _ _ |
...... +-----+
n=1: . | . _ | -> (100)(000)
...... | _ _ | .. -> 100000[bin] = 32 = a(1)
...... | _ _ |
...... +-----+
n=2: . | . _ | -> (110)(000)
...... | . _ | .. -> 110000[bin] = 48 = a(2)
...... | _ _ |
...... +-----+
n=3: . | . . | -> (100)(100)
...... | _ _ | .. -> 100100[bin] = 36 = a(3)
...... | _ _ |
...... +-----+
n=4: . | . . | -> (100)(110)
...... | _ . | .. -> 100110[bin] = 38 = a(4)
...... | _ _ |
...... +-----+
n=5: . | . _ | -> (100)(010)
...... | _ . | .. -> 100100[bin] = 34 = a(5)
...... | _ _ |
...... +-----+
n=6: . | . . | -> (110)(100)
...... | . _ | .. -> 111000[bin] = 52 = a(6)
...... | _ _ |
...... +-----+
n=7: . | . . | -> (110)(110)
...... | . . | .. -> 110110[bin] = 54 = a(7)
...... | _ _ |
...... +-----+
n=8: . | . _ | -> (110)(010)
...... | . . | .. -> 101100[bin] = 50 = a(8)
...... | _ _ |
...... +-----+
n=9: . | _ . | -> (010)(100)
...... | . _ | .. -> 010100[bin] = 20 = a(9)
...... | _ _ |
...... +-----+.

Links

Crossrefs

Cf. A121018.

Programs

  • Mathematica
    a[0]=22; a[1]= 32; a[2]= 48; a[3]= 36; a[4]= 38; a[5]= 34; a[6]= 52; a[7]= 54; a[8]= 50; a[9]=20; a[n_]:=a[Floor[n/10]]*64+a[Mod[n, 10]]; Table[a[n], {n, 0, 45}] (* James C. McMahon, Oct 12 2024 *)

Formula

a(n) = a(floor(n/10))*64 + a(n mod 10) for n>9.

A079405 Number of dots in primes in Braille.

Original entry on oeis.org

2, 2, 2, 4, 2, 3, 5, 3, 4, 4, 3, 6, 4, 5, 7, 4, 4, 4, 7, 5, 6, 6, 5, 5, 6, 5, 6, 8, 6, 4, 7, 4, 7, 5, 6, 4, 7, 6, 8, 7, 7, 5, 4, 5, 7, 5, 4, 6, 8, 6, 6, 6, 6, 5, 8, 7, 7, 7, 10, 6, 7, 6, 9, 4, 5, 7, 5, 8, 9, 7, 6, 6, 9, 8, 8, 7, 7, 8, 7, 8, 6, 6, 6, 7, 7, 8, 8, 9, 7, 8, 10, 9, 10, 6, 7, 7, 7, 5, 6, 6, 9, 8, 7, 7
Offset: 0

Views

Author

Jon Perry, Feb 16 2003

Keywords

Examples

			The 5th prime is 11, hence a(11)=1+1=2

Links

Crossrefs

Cf. A079399, A072283.

Programs

  • PARI
    { braille=[3,1,2,2,3,2,3,4,3,2]; forprime (n=2,300, b=braille[n%10+1]; n2=n; if (n>99, b=b+braille[n\100+1]; n2=n%100); if (n2>9,b=b+braille[n2\10+1]); print1(b",")) }
  • PARI
    { braille=[3, 1, 2, 2, 3, 2, 3, 4, 3, 2]; forprime (n=2, 300, n2=n; b=0; while (n2>0, b=b+braille[n2%10+1]; n2=n2\10); print1(b", ")) } \\ Sean A. Irvine, Feb 04 2010

Extensions

Corrected and extended by Sean A. Irvine, Feb 04 2010

A238365 Number of dots needed to express n as a Roman numeral in Braille.

Original entry on oeis.org

2, 4, 6, 6, 4, 6, 8, 10, 6, 4, 6, 8, 10, 10, 8, 10, 12, 14, 10, 8, 10, 12, 14, 14, 12, 14, 16, 18, 14, 12, 14, 16, 18, 18, 16, 18, 20, 22, 18, 7, 9, 11, 13, 13, 11, 13, 15, 17, 13, 3, 5, 7, 9, 9, 7, 9, 11, 13, 9, 7, 9, 11, 13, 13, 11, 13, 15, 17, 13, 11, 13, 15
Offset: 1

Views

Author

Arkadiusz Wesolowski, Feb 25 2014

Keywords

Examples

			VII in Braille (with the "Roman num" character):
  o  o      o    o
     o    o    o
  o  o o
Therefore a(7) = 10 - 2 = 8.

Links

Crossrefs

Cf. also A002963, A048181, A030166, A072283, A079399, A121018, A220090.

Programs

  • PARI
    a=[2, 4, 6, 6, 4, 6, 8, 10, 6, 0]; b=[0, 4, 8, 12, 7, 3, 7, 11, 15, 6]; for(n=1, 72, if(n<100, print1(a[lift(Mod(n-1, 10))+1]+b[floor(n/10)+1], ", "), break));
  • PARI
    /* The program works for n < 40 */
b=0; for(n=1, 39, if(Mod(n, 10)==0, b=b+4); m=lift(Mod(n, 10)); a=2*m-6; if(Mod(m, 5)==4, d=abs(a-7)+b+1, if(m<4, d=a+b+6, d=a+b)); print1(d, ", "));
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.