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 1-2 of 2 results.

A219031 Table read by rows: n-th row lists all distinct subwords of decimal representation of n-th square.

Original entry on oeis.org

0, 1, 4, 9, 1, 6, 16, 2, 5, 25, 3, 6, 36, 4, 9, 49, 4, 6, 64, 1, 8, 81, 0, 1, 10, 100, 1, 2, 12, 21, 121, 1, 4, 14, 44, 144, 1, 6, 9, 16, 69, 169, 1, 6, 9, 19, 96, 196, 2, 5, 22, 25, 225, 2, 5, 6, 25, 56, 256, 2, 8, 9, 28, 89, 289, 2, 3, 4, 24, 32, 324, 1, 3
Offset: 0

Views

Author

Reinhard Zumkeller, Nov 10 2012

Keywords

Comments

A219032(n) gives number of squares in n-th row.

Examples

			First 50 rows of triangle:
.   0: [0]                      .  25: [2,5,6,25,62,625]
.   1: [1]                      .  26: [6,7,67,76,676]
.   2: [4]                      .  27: [2,7,9,29,72,729]
.   3: [9]                      .  28: [4,7,8,78,84,784]
.   4: [1,6,16]                 .  29: [1,4,8,41,84,841]
.   5: [2,5,25]                 .  30: [0,9,90,900]
.   6: [3,6,36]                 .  31: [1,6,9,61,96,961]
.   7: [4,9,49]                 .  32: [0,1,2,4,10,24,102,1024]
.   8: [4,6,64]                 .  33: [0,1,8,9,10,89,108,1089]
.   9: [1,8,81]                 .  34: [1,5,6,11,15,56,115,156,1156]
.  10: [0,1,10,100]             .  35: [1,2,5,12,22,25,122,225,1225]
.  11: [1,2,12,21,121]          .  36: [1,2,6,9,12,29,96,129,296,1296]
.  12: [1,4,14,44,144]          .  37: [1,3,6,9,13,36,69,136,369,1369]
.  13: [1,6,9,16,69,169]        .  38: [1,4,14,44,144,444,1444]
.  14: [1,6,9,19,96,196]        .  39: [1,2,5,15,21,52,152,521,1521]
.  15: [2,5,22,25,225]          .  40: [0,1,6,16,60,160,600,1600]
.  16: [2,5,6,25,56,256]        .  41: [1,6,8,16,68,81,168,681,1681]
.  17: [2,8,9,28,89,289]        .  42: [1,4,6,7,17,64,76,176,764,1764]
.  18: [2,3,4,24,32,324]        .  43: [1,4,8,9,18,49,84,184,849,1849]
.  19: [1,3,6,36,61,361]        .  44: [1,3,6,9,19,36,93,193,936,1936]
.  20: [0,4,40,400]             .  45: [0,2,5,20,25,202,2025]
.  21: [1,4,41,44,441]          .  46: [1,2,6,11,16,21,116,211,2116]
.  22: [4,8,48,84,484]          .  47: [0,2,9,20,22,209,220,2209]
.  23: [2,5,9,29,52,529]        .  48: [0,2,3,4,23,30,230,304,2304]
.  24: [5,6,7,57,76,576]        .  49: [0,1,2,4,24,40,240,401,2401] .

Links

Crossrefs

Cf. A218978, A000290.

Programs

  • Haskell
    a219031 n k = a219031_tabf !! n !! k
a219031_row n = a219031_tabf !! n
a219031_tabf = map a218978_row a000290_list

A348467 The number of distinct decimal representations of integers embedded as slices in the decimal representation of n!.

Original entry on oeis.org

1, 1, 1, 1, 3, 6, 6, 7, 11, 20, 25, 33, 32, 41, 60, 72, 80, 106, 104, 132, 140, 150, 173, 239, 241, 269, 306, 344, 369, 440, 487, 542, 550, 639, 639, 754, 799, 840, 777, 932, 1094, 1032, 1129, 1203, 1376, 1440, 1386, 1681, 1700, 1737, 1700, 1948, 1964, 2099, 2219
Offset: 0

Views

Author

Peter Luschny, Oct 19 2021

Keywords

Examples

			0:  1 // 1;
1:  1 // 1;
2:  1 // 2;
3:  1 // 6;
4:  3 // 2,4,24;
5:  6 // 0,1,2,12,20,120;
6:  6 // 0,2,7,20,72,720;
7:  7 // 0,4,5,40,50,504,5040;
8: 11 // 0,2,3,4,20,32,40,320,403,4032,40320;
9: 20 // 0,2,3,6,8,28,36,62,80,88,288,362,628,880,2880,3628,6288,36288,62880, 362880.

Crossrefs

Cf. A120004, A219032, A000142.

Programs

  • Mathematica
    a[n_] := Length@ DeleteDuplicates[FromDigits /@ Rest@ Subsequences[ IntegerDigits[n!]]]; Array[a, 50, 0] (* Amiram Eldar, Oct 19 2021 *)
  • PARI
    f(n) = if (n==0, return (1)); my(d=digits(n), list=List()); for (k=1, #d, for (j=1, #d-k+1, my(dk=vector(j, i, d[k+i-1])); listput(list, fromdigits(dk)););); #Set(list); \\ A120004
a(n) = f(n!); \\ Michel Marcus, Oct 19 2021
  • Python
    from math import factorial
def A348467(n):
    s = str(factorial(n))
    m = len(s)
    return len(set(int(s[i:j]) for i in range(m) for j in range(i+1,m+1))) # Chai Wah Wu, Oct 19 2021

Formula

a(n) = A120004(n!). - Michel Marcus, Oct 19 2021
Showing 1-2 of 2 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.