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A027723 Palindromes of form k^2 + k + 7. 4
7, 9, 313, 999, 31513, 75357, 78687, 90909, 98289, 3159513, 7642467, 9009009, 743080347, 900090009, 31413131413, 90000900009, 97474147479, 3105075705013, 9000009000009, 757082131280757, 900000090000009, 907340818043709, 90000000900000009, 92269201110296229 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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)

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

CROSSREFS

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

Sequence in context: A012252 A262538 A306184 * A046265 A082705 A122577

Adjacent sequences:  A027720 A027721 A027722 * A027724 A027725 A027726

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

EXTENSIONS

More terms from Giovanni Resta, Aug 28 2018

STATUS

approved

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Last modified June 27 19:31 EDT 2022. Contains 354898 sequences. (Running on oeis4.)