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.

A082722 Numbers k for which there exist no palindromic 9-gonals (also known as nonagonals or enneagonals) of length k.

Original entry on oeis.org

2, 6, 13, 14, 15, 16, 20, 25, 27, 28, 29, 30, 31, 32
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Comments

Previous name was: There exist no palindromic nonagonals (enneagonals) of length n.

Links

Crossrefs

Cf. A034822, A059868, A082721, A059869, A059870, A034307.

Programs

  • Mathematica
    A082723 = {0, 1, 9, 111, 474, 969, 6666, 18981, 67276, 4411144, 6964696, 15444451, 57966975, 448707844, 460595064, 579696975, 931929139, 994040499, 1227667221, 9698998969, 61556965516, 664248842466, 699030030996, 99451743334715499, 428987160061789824, 950178723327871059, 1757445628265447571, 4404972454542794044, 9433971680861793349, 499583536595635385994, 1637992008558002997361, 19874891310701319847891};
A082722[n_] := Length[Select[A082723, IntegerLength[#] == n || (n == 1 && # == 0) &]];
Select[Range[22], A082722[#] == 0 &] (* Robert Price, Apr 29 2019 *)

Extensions

Definition edited by Jon E. Schoenfield, Sep 15 2013

A055560 Base numbers of 9-gonal palindromic numbers.

Original entry on oeis.org

1, 2, 6, 12, 17, 44, 74, 139, 1123, 1411, 2101, 4070, 11323, 11472, 12870, 16318, 16853, 18729, 52642, 132619, 435644, 446904, 168566853, 350096787, 521037077, 708609429, 1121857192, 1641773578, 11947307367, 21633254881, 75356090494
Offset: 1

Views

Author

J. Lowell, Jul 10 2000

Keywords

Links

Crossrefs

Cf. A001106, A082723.

Programs

  • Mathematica
    Select[Range[0, 10^5], PalindromeQ[PolygonalNumber[9, #]] &] (* Robert Price, Apr 29 2019 *)

Formula

9-gonal numbers are of the form (n(7n-5))/2.

Extensions

Edited and extended by Patrick De Geest, Apr 13 2003.

A307827 Palindromic decagonal (or 10-gonal) numbers.

Original entry on oeis.org

0, 1, 232, 27972, 76867, 25555552, 7154664517, 158229922851, 2028787878202, 2040061600402, 2733623263372, 52667666676625, 675972505279576, 28519896169891582, 73542836563824537, 74529570707592547, 25552469511596425552, 27835145788754153872
Offset: 1

Views

Author

Robert Price, Apr 30 2019

Keywords

Links

Crossrefs

Cf. A001107, A082723.

Programs

  • Mathematica
    Select[PolygonalNumber[10, Range[0, 10^5]], PalindromeQ]

A307829 Base numbers of decagonal (10-gonal) palindromic numbers.

Original entry on oeis.org

0, 1, 8, 84, 139, 2528, 42293, 198891, 712178, 714154, 826684, 3628625, 12999736, 84439174, 135593913, 136500523, 2527472528, 2637951184, 3960451966, 4094127596, 4415308953, 5192254461
Offset: 1

Views

Author

Robert Price, Apr 30 2019

Keywords

Links

Crossrefs

Cf. A001106, A082723, A055560.

Programs

  • Mathematica
    Select[Range[0, 10^5], PalindromeQ[PolygonalNumber[10, #]] &]

A307807 Number of palindromic nonagonal numbers with exactly n digits.

Original entry on oeis.org

3, 0, 3, 1, 2, 0, 2, 2, 5, 2, 1, 2, 0, 0, 0, 0, 1, 2, 3, 0, 1, 1
Offset: 1

Views

Author

Robert Price, Apr 29 2019

Keywords

Comments

Number of terms in A082723 with exactly n digits.

Examples

			There are only three 3 digit nonagonal numbers that are palindromic, 111, 474 and 969.  Thus, a(3)=3.

Links

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

Crossrefs

Cf. A001106, A055560, A082722, A082733, A307801, A307802.

Programs

  • Mathematica
    A082723 = {0, 1, 9, 111, 474, 969, 6666, 18981, 67276, 4411144, 6964696, 15444451, 57966975, 448707844, 460595064, 579696975, 931929139, 994040499, 1227667221, 9698998969, 61556965516, 664248842466, 699030030996, 99451743334715499, 428987160061789824, 950178723327871059, 1757445628265447571, 4404972454542794044, 9433971680861793349, 499583536595635385994, 1637992008558002997361, 19874891310701319847891}; Table[Length[Select[A082723, IntegerLength[#] == n || (n == 1 && # == 0) &]], {n, 22}]

A307808 Number of palindromic nonagonal numbers of length n whose index is also palindromic.

Original entry on oeis.org

3, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
Offset: 1

Views

Author

Robert Price, Apr 29 2019

Keywords

Comments

Is there a nonzero term beyond a(4)?

Examples

			There is only one palindromic nonagonal number of length 4 whose index is also palindromic, 44->6666. Thus, a(4)=1.

Links

Crossrefs

Cf. A001106, A055560, A082722, A082733, A307801, A307802.

Programs

  • Mathematica
    A082723 = {0, 1, 9, 111, 474, 969, 6666, 18981, 67276, 4411144, 6964696, 15444451, 57966975, 448707844, 460595064, 579696975, 931929139, 994040499, 1227667221, 9698998969, 61556965516, 664248842466, 699030030996, 99451743334715499, 428987160061789824, 950178723327871059, 1757445628265447571, 4404972454542794044, 9433971680861793349, 499583536595635385994, 1637992008558002997361, 19874891310701319847891};
A055560 = {0, 1, 2, 6, 12, 17, 44, 74, 139, 1123, 1411, 2101, 4070, 11323, 11472, 12870, 16318, 16853, 18729, 52642, 132619, 435644, 446904, 168566853, 350096787, 521037077, 708609429, 1121857192, 1641773578, 11947307367, 21633254881, 75356090494};
Table[Length[Select[A055560[[Table[Select[Range[22], IntegerLength[A082723[[#]]] ==  n || (n == 1 && A082723[[#]] == 0) &], {n, 22}][[n]]]], PalindromeQ[#] &]], {n, 22}]
Showing 1-6 of 6 results.

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