A027721 -id:A027721 - cp's OEIS frontend

A027723 Palindromes of form k^2 + k + 7.

7, 9, 313, 999, 31513, 75357, 78687, 90909, 98289, 3159513, 7642467, 9009009, 743080347, 900090009, 31413131413, 90000900009, 97474147479, 3105075705013, 9000009000009, 757082131280757, 900000090000009, 907340818043709, 90000000900000009, 92269201110296229

Offset: 1

Patrick De Geest

From Robert Israel, May 16 2018: (Start)
Palindromes m such that 4*m - 27 is a square.
Each term has an odd number of digits and ends in 3, 7 or 9.
Contains 9*(1+10^k+10^(2*k)) for each k>=1. (End)

Giovanni Resta, Table of n, a(n) for n = 1..45
P. De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X)

Cf. A027722, A027692, A027756, A005471, A027721, A027725.

R[1]:= [1,3,5,7,9]: X[1]:= R[1]:
for k from 2 to 6 do
  R[k]:= map(t -> seq(10^(k-1)*j+t,j=0..9),R[k-1]);
X[k]:= map(t -> seq(j+10*t,j=0..9),X[k-1])
od:
Res:= 7,9:
for k from 1 to 6 do
  for j from 1 to 5*10^(k-1) do
      r:= 10^(k+1)*X[k][j]+R[k][j];
      for y from 0 to 9 do
        if issqr(4*(r+10^k*y)-27) then
          x:= r+10^k*y;
          Res:= Res,x;
        fi
od od od:
Res; # Robert Israel, May 16 2018

More terms from Giovanni Resta, Aug 28 2018

A027728 Palindromes of form k^2 + k + 5.

Original entry on oeis.org

5, 7, 11, 77, 161, 707, 5555, 16261, 50405, 53135, 7570757, 11988911, 16100161, 16544561, 162626261, 502858205, 758919857, 793464397, 11092829011, 11539593511, 5560873780655, 7424090904247, 7702753572077, 16515222251561, 57293477439275, 7246424554246427

Offset: 1

Patrick De Geest

Giovanni Resta, Table of n, a(n) for n = 1..46
P. De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X)

Cf. A027718, A027690, A027754, A027755, A027717, A027728, A027721.

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse[d]]; f[n_] := n^2 + n + 5; Select[f@ Range[0, 10^5], palQ] (* Giovanni Resta, Aug 29 2018 *)
Select[Table[k^2+k+5,{k,0,852*10^5}],PalindromeQ] (* Harvey P. Dale, Aug 04 2025 *)

More terms from Giovanni Resta, Aug 28 2018

A027729 Numbers k such that k^2+k+6 is a palindrome.

Original entry on oeis.org

0, 1, 24, 25, 28, 288, 2485, 2550, 2888, 2946, 28888, 146777, 264334, 288888, 292276, 2834101, 2873233, 2888888, 2952316, 2960816, 2985943, 2995631, 14604657, 16353547, 28888888, 29190748, 29585508, 148278137, 264056434, 288888888, 2853889203, 2931604151, 28988127118

Offset: 1

Patrick De Geest

Patrick De Geest, Palindromic Quasi_Over_Squares of the form n^2+(n+X)

Cf. A027721, A027691, A027718, A027722.

[n: n in [0..3*10^6] | Intseq(n^2+n+6) eq Reverse(Intseq(n^2+n+6))]; // Vincenzo Librandi, Jun 16 2016

palOblongPlus6Q[n_] := Module[{d = IntegerDigits[n^2 + n + 6]}, d == Reverse[d]]; Select[Range[0, 3000000],  palOblongPlus6Q] (* Harvey P. Dale, Nov 14 2012 *)

a(23)-a(33) from Giovanni Resta, Aug 27 2018

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A027723 Palindromes of form k^2 + k + 7.

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A027728 Palindromes of form k^2 + k + 5.

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A027729 Numbers k such that k^2+k+6 is a palindrome.

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