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A027723
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Palindromes of form k^2 + k + 7.
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4
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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
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1,1
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COMMENTS
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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)
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LINKS
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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)
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MAPLE
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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
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CROSSREFS
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Cf. A027722, A027692, A027756, A005471, A027721, A027725.
Sequence in context: A012252 A262538 A306184 * A046265 A082705 A122577
Adjacent sequences: A027720 A027721 A027722 * A027724 A027725 A027726
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KEYWORD
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nonn,base
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AUTHOR
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Patrick De Geest
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EXTENSIONS
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More terms from Giovanni Resta, Aug 28 2018
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STATUS
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approved
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