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.

A035090 Non-palindromic squares which when written backwards remain square (and still have the same number of digits).

Original entry on oeis.org

144, 169, 441, 961, 1089, 9801, 10404, 10609, 12544, 12769, 14884, 40401, 44521, 48841, 90601, 96721, 1004004, 1006009, 1022121, 1024144, 1026169, 1042441, 1044484, 1062961, 1212201, 1214404, 1216609, 1236544, 1238769, 1256641
Offset: 1

Views

Author

Patrick De Geest, Nov 15 1998

Keywords

Comments

Squares with trailing zeros not included.
Sequence is infinite, since it includes, e.g., 10^(2k) + 4*10^k + 4 for all k. - Robert Israel, Sep 20 2015

Links

Crossrefs

Reversing a polytopal number gives a polytopal number:
cube to cube: A035123, A035124, A035125, A002781;
square to square: A161902, A035090, A033294, A106323, A106324, A002779;
square to triangular: A181412, A066702;
tetrahedral to tetrahedral: A006030;
triangular to square: A066703, A179889;
triangular to triangular: A066528, A069673, A003098, A066569.
Cf. A319388.

Programs

  • Maple
    rev:= proc(n) local L,i;
L:= convert(n,base,10);
add(L[-i]*10^(i-1),i=1..nops(L))
end proc:
filter:= proc(n) local t;
  if n mod 10 = 0 then return false fi;
  t:= rev(n);
t <> n and issqr(t)
end proc:
select(filter, [seq(n^2, n=1..10^5)]); # Robert Israel, Sep 20 2015
  • Mathematica
    Select[Range[1200]^2,!PalindromeQ[#]&&IntegerLength[#]==IntegerLength[ IntegerReverse[ #]] && IntegerQ[Sqrt[IntegerReverse[#]]]&] (* Harvey P. Dale, Jul 19 2023 *)

Formula

a(n) = A035123(n)^2. - R. J. Mathar, Jan 25 2017

A069673 Nonpalindromic triangular numbers whose digit reversal is also a triangular number (possibly with fewer digits).

Original entry on oeis.org

10, 120, 153, 190, 300, 351, 630, 820, 17578, 87571, 156520, 180300, 185745, 547581, 557040, 678030, 1461195, 1851850, 5911641, 6056940, 12145056, 12517506, 16678200, 56440000, 60571521, 65054121, 157433640, 188267310, 304119453, 354911403, 1261250200
Offset: 1

Views

Author

Amarnath Murthy, Apr 06 2002

Keywords

Links

Crossrefs

See A066528 for a different version.
Cf. A066703, A179889.
Cf. A003098, A061455, A066569.

Extensions

More terms from Jason Earls, Jun 07 2002
a(27)-a(31) from Giovanni Resta, Jun 20 2015

A066528 Non-palindromic triangular numbers whose reverse is a triangular number with the same number of digits.

Original entry on oeis.org

153, 351, 17578, 87571, 185745, 547581, 1461195, 5911641, 12145056, 12517506, 60571521, 65054121, 304119453, 354911403, 1775275491, 1945725771, 10246462281, 17990863516, 18226464201, 35615002605, 50620051653, 61536809971, 1222080857271, 1664224065406
Offset: 1

Views

Author

Erich Friedman, Jan 08 2002

Keywords

Examples

			153 and 351 are both triangular.

Links

Crossrefs

See A069673 for another version.
Cf. A066703, A179889.
Cf. A003098, A061455, A066569, A069673.

Programs

  • Mathematica
    dtn[L_] := Fold[10#1+#2&, 0, L]; tritest[n_] := Module[{t}, t=Floor[N[Sqrt[2n]]]; 2n==t(t+1)]; A={}; For[i=1, i>0, i++, t=i(i+1)/2; If[tritest[tt=dtn[Reverse[IntegerDigits[t]]]]&&Mod[t, 10]>0&&t=!=tt, AppendTo[A, t]; Print[A]]]

Extensions

a(22)-a(24) from Giovanni Resta, Jun 20 2015

A179889 Triangular numbers whose reverse is a square (possibly with fewer digits).

Original entry on oeis.org

1, 10, 630, 52650, 165600, 986310, 9446031, 9485190, 10693000, 1270004401, 14214075921, 140884670790, 1809702709101, 4614899724711, 6766532724546, 9802814901400, 10210140486640, 14287075542460, 52657436563056, 98855178542676
Offset: 1

Views

Author

Harvey P. Dale, Jan 30 2011

Keywords

Examples

			9446031 is triangular and 1306449 is a square.

Links

Crossrefs

A variant of A066703. Cf. A069673, A181412, A066528.

Programs

  • Mathematica
    trnos=Accumulate[Range[14070000]];
sqnoQ[n_]:=IntegerQ[Sqrt[FromDigits[Reverse[IntegerDigits[n]]]]]
Select[trnos,sqnoQ]  (* Harvey P. Dale, Jan 31 2011 *)

Extensions

More terms from Harvey P. Dale, Jan 31 2011

A181412 Squares whose reverse is a triangular number; trailing zeros are permitted.

Original entry on oeis.org

1, 100, 10000, 1000000, 1306449, 100000000, 130644900, 1044000721, 10000000000, 12957041241, 13064490000, 104400072100, 1000000000000, 1019072079081, 1174279984164, 1295704124100, 1306449000000, 6454272356676, 10440007210000
Offset: 1

Views

Author

Harvey P. Dale, Jan 30 2011

Keywords

Comments

Suggested by T. D. Noe.

Examples

			1306449 is 1143 squared, and its reverse, 9446031, is a triangular number.

Links

Crossrefs

Cf. A066702, A001110, A066703, A179889, A066528, A069673.

Programs

  • Mathematica
    trnos = Accumulate[Range[300000]]; Select[Range[210000]^2, MemberQ[trnos, FromDigits[Reverse[IntegerDigits[#]]]] &]

Extensions

a(12)-a(19) from Donovan Johnson, Feb 12 2011

A066702 Square numbers whose reverse is triangular with the same number of digits.

Original entry on oeis.org

0, 1, 1306449, 1044000721, 12957041241, 1019072079081, 1174279984164, 6454272356676, 65036563475625, 67624587155889, 123826990849454025, 170448128872993657764, 19198191503444720114404
Offset: 1

Views

Author

Erich Friedman, Jan 14 2002

Keywords

Comments

The sequence of corresponding triangular numbers is A066703. - Robert G. Wilson v, Jan 31 2011

Examples

			9446031 is triangular and 1306449 is a square.

Crossrefs

Cf. A066703, A181412. - Harvey P. Dale, Jan 30 2011

Programs

  • Mathematica
    lst = {0}; For[i = 1, i > 0, i++, s = i^2; t = FromDigits@ Reverse@ IntegerDigits@ s; If[ IntegerQ@ Sqrt[8 t + 1] && Mod[s, 10] > 0, AppendTo[lst, s]; Print@ lst]]

Extensions

a(12)-a(13) from and offset corrected by Giovanni Resta, Jun 20 2015
Showing 1-6 of 6 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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