|
|
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
|
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
|
|
|
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:
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|