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.

Previous Showing 11-16 of 16 results.

A229236 Palindromic triangular number with palindromic index.

Original entry on oeis.org

1, 3, 6, 66, 3003, 66066, 617716, 3544453, 6172882716, 30416261403, 61728399382716, 66056806460865066, 3549632679762369453, 354963215686512369453, 30416741529792514761403, 35496321045754012369453, 3041674104186814014761403
Offset: 1

Views

Author

Shyam Sunder Gupta, Sep 17 2013

Keywords

Examples

			a(5)=3003 because 3003 is 77th triangular number and 77 is palindrome.

Links

Crossrefs

Cf. A003098, A000217, A008509, A008510.

Programs

  • Mathematica
    Select[Table[{n,(n(n+1))/2},{n,10^8}],AllTrue[#,PalindromeQ]&][[;;,2]] (* Harvey P. Dale, Jun 04 2023 *)

Extensions

Previous Mathematica program replaced by Harvey P. Dale, Jun 04 2023

A307348 Numbers k such that there are no palindromic triangular numbers of length k.

Original entry on oeis.org

12, 30, 40
Offset: 1

Views

Author

Robert Price, May 01 2019

Keywords

Links

Crossrefs

Cf. A000217, A003098, A008509, A034822.

Programs

  • Mathematica
    A003098 = Select[PolygonalNumber[3, Range[0, 10^6]], PalindromeQ];
(* Set Range to level of desired running time. *)
nopal[n_] := Length[Select[A003098, IntegerLength[#] == n || (n == 1 && # == 0) &]]; Select[Range[12], nopal[#] == 0 &]
(* Set Range to encompass length of last value in A003098. *)

A089717 Triangular numbers with palindromic indices.

Original entry on oeis.org

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 66, 253, 561, 990, 1540, 2211, 3003, 3916, 4950, 5151, 6216, 7381, 8646, 10011, 11476, 13041, 14706, 16471, 18336, 20503, 22578, 24753, 27028, 29403, 31878, 34453, 37128, 39903, 42778, 46056, 49141, 52326, 55611
Offset: 1

Views

Author

Giovanni Teofilatto, Nov 24 2004

Keywords

Links

Crossrefs

Cf. A008509, A000217, A002113.

Programs

  • Mathematica
    Module[{nn=500,paldx},paldx=Table[If[PalindromeQ[n],1,0],{n,0,nn}];Pick[Accumulate[ Range[ 0,nn]],paldx,1]] (* Harvey P. Dale, Jun 11 2024 *)
  • Python
    from itertools import chain, count, islice
def A089717_gen(): # generator of terms
    return map(lambda n:n*(n+1)//2,chain((0,),chain.from_iterable(chain((int((s:=str(d))+s[-2::-1]) for d in range(10**l,10**(l+1))), (int((s:=str(d))+s[::-1]) for d in range(10**l,10**(l+1)))) for l in count(0))))
A089717_list = list(islice(A089717_gen(),20)) # Chai Wah Wu, Jun 23 2022

Formula

a(n) = A000217(A002113(n)).

Extensions

Definition corrected by Lambert.Klasen and David Wasserman, Oct 04 2005
More terms from David Wasserman and Klaus Brockhaus, Oct 04 2005

A307367 Number of palindromic triangular numbers with exactly n digits.

Original entry on oeis.org

4, 2, 3, 3, 2, 2, 6, 2, 1, 4, 7, 0, 4, 4, 12, 5, 6, 2, 3, 2, 6, 3, 6, 2, 2, 4, 3, 2, 5, 0, 3, 2, 1, 4, 3, 1, 10, 1, 4, 0, 3, 2, 2, 1, 1
Offset: 1

Views

Author

Robert Price, May 01 2019

Keywords

Comments

Number of terms in A003098 with exactly n digits.
Differs from A054263 only at a(1), assuming 0 has 1 digits. - R. J. Mathar, May 06 2019

Links

  • G. J. Simmons, Palindromic powers, J. Rec. Math., 3 (No. 2, 1970), 93-98. [Annotated scanned copy] See page 95.

Crossrefs

Cf. A000217, A003098, A008509, A034822, A263618, A307348.

Programs

  • Mathematica
    A003098 = Select[PolygonalNumber[3, Range[0, 10^6]], PalindromeQ];
  (* Set Range to level of desired running time. \ *)
Table[Length[ Select[A003098, IntegerLength[#] == n || (n == 1 && # == 0) &]], {n, 12}]
  (* Set Range to encompass length of last value in A003098. *)

A101034 Numbers n such that A002113(n) is a triangular number.

Original entry on oeis.org

0, 1, 3, 6, 14, 15, 26, 68, 75, 129, 158, 186, 249, 759, 1616, 1827, 2268, 2679, 4543, 6072, 6675, 7294, 13512, 16146, 27871, 112640, 116339, 152889, 161727, 239533, 260487, 404161, 670038, 685744, 767718, 973504, 2313206, 6250177, 6977617
Offset: 1

Views

Author

Klaus Brockhaus, Nov 27 2004

Keywords

Comments

Indices of triangular numbers in the sequence of palindromes.

Examples

			A002113(26) = 171 is a triangular number, so 26 is a term.

Crossrefs

Cf. A000217, A002113, A003098, A008509.

Programs

Extensions

a(24) to a(38) from Klaus Brockhaus, Oct 05 2005

A307850 Number of palindromic triangular numbers of length n whose index is also palindromic.

Original entry on oeis.org

4, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Robert Price, May 01 2019

Keywords

Examples

			There is only one palindromic triangular number of length 2 whose index is also palindromic. 11->66. Thus, a(2)=1.

Links

Crossrefs

Cf. A000217, A003098, A008509, A307348, A307367.

Programs

  • Mathematica
    A003098 = Select[PolygonalNumber[3, Range[0, 10^6]], PalindromeQ]
  (* Set Range to level of desired running time. *)
A008509 = Select[Range[0, 10^6], PalindromeQ[PolygonalNumber[3, #]] &]
  (* Set Range to level of desired running time. *)
Table[Length[ Select[A008509[[Table[ Select[Range[35], IntegerLength[A003098[[#]]] == n || (n == 1 && A003098[[#]] == 0) &], {35}][[n]]]], PalindromeQ[#] &]], {n, 11}]
  (* Set the first two Ranges to encompass the length of A003098 and  the last Range to encompass the length of the last value in A003098. *)
Previous Showing 11-16 of 16 results.

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