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 1-4 of 4 results.

A082721 There exist no palindromic hexagonals of length n.

Original entry on oeis.org

3, 8, 9, 12, 22, 24, 27, 30, 36, 38, 40
Offset: 1

Views

Author

Patrick De Geest, Apr 13 2003

Keywords

Links

Crossrefs

Cf. A034822, A054969, A059868, A059869, A059870, A082722, A034307.

Programs

  • Mathematica
    A054969 = {0, 1, 6, 66, 3003, 5995, 15051, 66066, 617716, 828828, 1269621, 1680861, 5073705, 5676765, 1264114621, 5289009825, 6172882716, 13953435931, 1313207023131, 5250178710525, 6874200024786, 61728399382716, 602224464422206, 636188414881636, 1250444114440521, 16588189498188561, 58183932923938185, 66056806460865066, 67898244444289876, 514816979979618415, 3075488771778845703, 6364000440440004636, 15199896744769899151};
A082721[n_] := Length[Select[A054969, IntegerLength[#] == n || (n == 1 && # == 0) &]];
Select[Range[19], A082721[#] == 0 &] (* Robert Price, Apr 27 2019 *)
  • Python
    def ispal(n): s = str(n); return s == s[::-1]
def hexpals(limit):
  yield from (k*(2*k-1) for k in range(limit+1) if ispal(k*(2*k-1)))
def aupto(limit):
  lengths = set(range(1, limit+1))
  for h in hexpals(10**limit):
    if len(lengths) == 0: return
    lh, minlen = len(str(h)), min(lengths)
    if lh > minlen: print(minlen, "in A082721"); lengths.discard(minlen)
    if lh in lengths: lengths.discard(lh); print("... discarding", lh)
aupto(14) # Michael S. Branicky, Mar 08 2021

A307830 Numbers k for which there exist no palindromic decagonal numbers (also known as 10-gonals) of length k.

Original entry on oeis.org

2, 4, 6, 7, 9, 11, 16, 18, 19
Offset: 1

Views

Author

Robert Price, Apr 30 2019

Keywords

Links

Crossrefs

Cf. A001107, A082722, A307827, A307829.

Programs

  • Mathematica
    A307827 = {0, 1, 232, 27972, 76867, 25555552, 7154664517, 158229922851, 2028787878202, 2040061600402, 2733623263372, 52667666676625, 675972505279576, 28519896169891582, 73542836563824537, 74529570707592547, 25552469511596425552, 27835145788754153872, 62740719088091704726, 67047523077032574076, 77979812588521897977, 107838025535520838701};
a[n_] := Length[Select[A307827, IntegerLength[#] == n || (n == 1 && # == 0) &]];
Select[Range[20], a[#] == 0 &]

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 1-4 of 4 results.

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