|
|
A108537
|
|
Concatenation of palindrome k and its 10's complement is prime.
|
|
1
|
|
|
1, 3, 7, 77, 99, 151, 161, 333, 707, 727, 737, 757, 949, 969, 989, 1441, 1551, 1771, 1881, 3003, 7227, 7667, 7997, 9009, 9339, 9999, 10001, 10101, 10701, 11111, 11611, 11711, 12221, 12921, 13231, 14341, 14841, 14941, 15851, 16661, 16961, 17071
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
EXAMPLE
|
a(7)=161 because 1000-161 = 839 and 161839 is prime.
|
|
MAPLE
|
N:= 5: # for terms of <= N digits
digrev:= proc(n) local L, i;
L:= convert(n, base, 10);
add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
Res:= 1, 3, 7, 9:
for d from 2 to N do
if d::even then
m:= d/2;
Res:= Res, seq(seq((i*10^(m-1)+j)*10^m + digrev(i*10^(m-1)+j), j=0..10^(m-1)-1), i=[1, 3, 7, 9]);
else
m:= (d-1)/2;
Res:= Res, seq(seq(seq((i*10^(m-1)+j)*10^(m+1)+y*10^m+digrev(i*10^(m-1)+j), y=0..9), j=0..10^(m-1)-1), i=[1, 3, 7, 9]);
fi
od:
filter:= proc(t) local r;
r:= 10^(ilog10(t)+1)-t;
isprime(t*10^(ilog10(r)+1)+r)
end proc:
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,easy,nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|