

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
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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^(k1)*j+t, j=0..9), R[k1]);
X[k]:= map(t > seq(j+10*t, j=0..9), X[k1])
od:
Res:= 7, 9:
for k from 1 to 6 do
for j from 1 to 5*10^(k1) 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



