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

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

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)

Links

• 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)

Crossrefs

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

Programs

Maple

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

Extensions

More terms from Giovanni Resta, Aug 28 2018