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 1-9 of 9 results.

A059805 Natural numbers written with digits grouped in pairs and leading zeros omitted.

Original entry on oeis.org

12, 34, 56, 78, 91, 1, 11, 21, 31, 41, 51, 61, 71, 81, 92, 2, 12, 22, 32, 42, 52, 62, 72, 82, 93, 3, 13, 23, 33, 43, 53, 63, 73, 83, 94, 4, 14, 24, 34, 44, 54, 64, 74, 84, 95, 5, 15, 25, 35, 45, 55, 65, 75, 85, 96, 6, 16, 26, 36, 46, 56, 66, 76, 86, 97, 7, 17, 27, 37, 47, 57, 67
Offset: 1

Views

Author

Kazimierz Kurz (kurzk(AT)prokom.pl), Mar 01 2001

Keywords

Links

Crossrefs

Cf. A000027, A087406, A060936, A087407, A087408, A087409, A087075, A087410, A087411.
Cf. A091331, A091332.

Programs

  • Mathematica
    FromDigits /@ Partition[ Flatten[ IntegerDigits[ Table[ n, {n, 1, 77}]]], 2] (* Robert G. Wilson v *)
FromDigits/@Partition[Flatten[IntegerDigits/@Range[100]],2] (* Harvey P. Dale, Feb 13 2025 *)
  • PARI
    {c=0; d=[]; for(n=1, 99, while(#d<2, d=concat(d, digits(c++))); print1(d[1],d[2]", "); d=vecextract(d, "^..2"))} \\ M. F. Hasler, Oct 23 2014

Formula

a(2n-1)*100 + a(2n) = A091332(n); a(2n-1) = floor(A091332(n)/100), a(2n) = (A091332(n) mod 100). - M. F. Hasler, Oct 23 2014

Extensions

More terms from Jason Earls, Mar 24 2001

A060923 Bisection of Lucas triangle A060922: even-indexed members of column sequences of A060922 (not counting leading zeros).

Original entry on oeis.org

1, 4, 1, 11, 17, 1, 29, 80, 39, 1, 76, 303, 315, 70, 1, 199, 1039, 1687, 905, 110, 1, 521, 3364, 7470, 6666, 2120, 159, 1, 1364, 10493, 29634, 37580, 20965, 4311, 217, 1, 3571, 31885, 109421, 181074, 148545
Offset: 0

Views

Author

Wolfdieter Lang, Apr 20 2001

Keywords

Examples

			Triangle begins:
  {1};
  {4,1};
  {11,17,1};
  {29,80,39,1};
  ...
pLe(2,x) = 1+11*x-11*x^2+4*x^3.

Crossrefs

Row sums give A060926.
Column sequences (without leading zeros) are, for m=0..3: A002878, A060934-A060936.
Companion triangle A060924 (odd part).
Cf. A060922.

Formula

a(n, m) = A060922(2*n-m, m).
a(n, m) = ((2*(n-m)+1)*A060924(n-1, m-1) + 2*(4*n-3*m)*a(n-1, m-1) + 4*(2*n-m-1)*A060924(n-2, m-1))/(5*m), m >= n >= 1; a(n, 0)= A002878(n); else 0.
G.f. for column m >= 0: x^m*pLe(m+1, x)/(1-3*x+x^2)^(m+1), where pLe(n, x) := Sum_{m=0..n+floor(n/2)} A061186(n, m)*x^m are the row polynomials of the (signed) staircase A061186.
T(n,k) = 3*T(n-1,k) + 2*T(n-1,k-1) - T(n-2,k) + 2*T(n-2,k-1) - T(n-2,k-2) + 4*T(n-3,k-2), T(0,0) = 1, T(1,0) = 4, T(1,1) = 1, T(2,0) = 11, T(2,1) = 17, T(2,2) = 1, T(n,k) = 0 if k < 0 or if k > n. - Philippe Deléham, Jan 21 2014

A087409 Multiples of 6 with digits grouped in pairs and leading zeros omitted.

Original entry on oeis.org

61, 21, 82, 43, 3, 64, 24, 85, 46, 6, 67, 27, 88, 49, 9, 61, 2, 10, 81, 14, 12, 1, 26, 13, 21, 38, 14, 41, 50, 15, 61, 62, 16, 81, 74, 18, 1, 86, 19, 21, 98, 20, 42, 10, 21, 62, 22, 22, 82, 34, 24, 2, 46, 25, 22, 58, 26, 42, 70, 27, 62, 82, 28, 82, 94, 30, 3, 6, 31, 23, 18, 32, 43
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2003

Keywords

Links

Crossrefs

Cf. A008588, A059805, A087406, A060936, A087407, A087408, A087075, A087410, A087411.

Programs

  • Mathematica
    FromDigits /@ Partition[ Flatten[ IntegerDigits[ Table[ 6n, {n, 1, 60}]]], 2] (* Robert G. Wilson v *)

Extensions

More terms from Ray Chandler, Oct 20 2003

A087075 Multiples of 7 with digits grouped in pairs and leading zeros omitted.

Original entry on oeis.org

71, 42, 12, 83, 54, 24, 95, 66, 37, 7, 78, 49, 19, 81, 5, 11, 21, 19, 12, 61, 33, 14, 1, 47, 15, 41, 61, 16, 81, 75, 18, 21, 89, 19, 62, 3, 21, 2, 17, 22, 42, 31, 23, 82, 45, 25, 22, 59, 26, 62, 73, 28, 2, 87, 29, 43, 1, 30, 83, 15, 32, 23, 29, 33, 63, 43, 35, 3, 57, 36, 43, 71
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2003

Keywords

Crossrefs

Cf. A008589, A059805, A087406, A060936, A087407, A087408, A087409, A087410, A087411.

Programs

  • Mathematica
    FromDigits /@ Partition[ Flatten[ IntegerDigits[ Table[ 7n, {n, 1, 60}]]], 2] (* Robert G. Wilson v *)
(IntegerDigits/@(7 Range[16]))//peek//Flatten//Partition[ #, 2]&// Map[FromDigits, # ]& (* Ken Levasseur *)

Extensions

More terms from Ray Chandler, Oct 20 2003

A087406 Multiples of 2 with digits grouped in pairs and leading zeros omitted.

Original entry on oeis.org

24, 68, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 10, 1, 2, 10, 41, 6, 10, 81, 10, 11, 21, 14, 11, 61, 18, 12, 1, 22, 12, 41, 26, 12, 81, 30
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2003

Keywords

Crossrefs

Cf. A005843, A059805, A060936, A087407, A087408, A087409, A087075, A087410, A087411.

Programs

  • Mathematica
    FromDigits /@ Partition[ Flatten[ IntegerDigits[ Table[ 2n, {n, 1, 65}]]], 2] (* Robert G. Wilson v *)
FromDigits/@Partition[Flatten[IntegerDigits/@(2*Range[80])],2] (* Harvey P. Dale, Apr 22 2022 *)

Extensions

More terms from Ray Chandler, Oct 20 2003

A087407 Multiples of 4 with digits grouped in pairs and leading zeros omitted.

Original entry on oeis.org

48, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 10, 1, 4, 10, 81, 12, 11, 61, 20, 12, 41, 28, 13, 21, 36, 14, 1, 44, 14, 81, 52, 15, 61, 60, 16, 41, 68, 17, 21, 76, 18, 1, 84, 18, 81, 92, 19, 62, 0, 20, 42, 8, 21, 22, 16, 22, 2, 24, 22
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2003

Keywords

Crossrefs

Cf. A008586, A059805, A087406, A060936, A087408, A087409, A087075, A087410, A087411.

Programs

  • Mathematica
    FromDigits /@ Partition[ Flatten[ IntegerDigits[ Table[ 4n, {n, 1, 60}]]], 2] (* Robert G. Wilson v *)

Extensions

More terms from Ray Chandler, Oct 20 2003

A087408 Multiples of 5 with digits grouped in pairs and leading zeros omitted.

Original entry on oeis.org

51, 1, 52, 2, 53, 3, 54, 4, 55, 5, 56, 6, 57, 7, 58, 8, 59, 9, 51, 0, 10, 51, 10, 11, 51, 20, 12, 51, 30, 13, 51, 40, 14, 51, 50, 15, 51, 60, 16, 51, 70, 17, 51, 80, 18, 51, 90, 19, 52, 0, 20, 52, 10, 21, 52, 20, 22, 52, 30, 23, 52, 40, 24, 52, 50, 25, 52, 60, 26, 52, 70, 27, 52, 80
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2003

Keywords

Crossrefs

Cf. A008587, A059805, A087406, A060936, A087407, A087409, A087075, A087410, A087411.

Programs

  • Mathematica
    FromDigits /@ Partition[ Flatten[ IntegerDigits[ Table[ 5n, {n, 1, 60}]]], 2] (* Robert G. Wilson v *)

Extensions

More terms from Ray Chandler, Oct 20 2003

A087410 Multiples of 8 with digits grouped in pairs and leading zeros omitted.

Original entry on oeis.org

81, 62, 43, 24, 4, 85, 66, 47, 28, 8, 89, 61, 4, 11, 21, 20, 12, 81, 36, 14, 41, 52, 16, 1, 68, 17, 61, 84, 19, 22, 0, 20, 82, 16, 22, 42, 32, 24, 2, 48, 25, 62, 64, 27, 22, 80, 28, 82, 96, 30, 43, 12, 32, 3, 28, 33, 63, 44, 35, 23, 60, 36, 83, 76, 38, 43, 92, 40, 4, 8, 41, 64, 24
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2003

Keywords

Crossrefs

Cf. A008590, A059805, A087406, A060936, A087407, A087408, A087409, A087075, A087411.

Programs

  • Mathematica
    FromDigits /@ Partition[ Flatten[ IntegerDigits[ Table[ 8n, {n, 1, 60}]]], 2] (* Robert G. Wilson v *)

Extensions

More terms from Ray Chandler, Oct 20 2003

A087411 Multiples of 9 with digits grouped in pairs and leading zeros omitted.

Original entry on oeis.org

91, 82, 73, 64, 55, 46, 37, 28, 19, 9, 91, 8, 11, 71, 26, 13, 51, 44, 15, 31, 62, 17, 11, 80, 18, 91, 98, 20, 72, 16, 22, 52, 34, 24, 32, 52, 26, 12, 70, 27, 92, 88, 29, 73, 6, 31, 53, 24, 33, 33, 42, 35, 13, 60, 36, 93, 78, 38, 73, 96, 40, 54, 14, 42, 34, 32, 44, 14, 50, 45, 94
Offset: 1

Views

Author

N. J. A. Sloane, Oct 19 2003

Keywords

Crossrefs

Cf. A008591, A059805, A087406, A060936, A087407, A087408, A087409, A087075, A087410.

Programs

  • Mathematica
    FromDigits /@ Partition[ Flatten[ IntegerDigits[ Table[ 9n, {n, 1, 60}]]], 2] (* Robert G. Wilson v *)

Extensions

More terms from Ray Chandler, Oct 20 2003
Showing 1-9 of 9 results.

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