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Concatenation of palindrome k and its 10's complement is prime.
1

%I #9 Jan 22 2019 17:30:46

%S 1,3,7,77,99,151,161,333,707,727,737,757,949,969,989,1441,1551,1771,

%T 1881,3003,7227,7667,7997,9009,9339,9999,10001,10101,10701,11111,

%U 11611,11711,12221,12921,13231,14341,14841,14941,15851,16661,16961,17071

%N Concatenation of palindrome k and its 10's complement is prime.

%C Contains 10^k-1 for k in A056696, and (10^k-1)/9 for k in A108966. - _Robert Israel_, Jan 22 2019

%H Robert Israel, <a href="/A108537/b108537.txt">Table of n, a(n) for n = 1..10000</a>

%e a(7)=161 because 1000-161 = 839 and 161839 is prime.

%p N:= 5: # for terms of <= N digits

%p digrev:= proc(n) local L,i;

%p L:= convert(n,base,10);

%p add(L[-i]*10^(i-1),i=1..nops(L))

%p end proc:

%p Res:= 1,3,7,9:

%p for d from 2 to N do

%p if d::even then

%p m:= d/2;

%p 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]);

%p else

%p m:= (d-1)/2;

%p 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]);

%p fi

%p od:

%p filter:= proc(t) local r;

%p r:= 10^(ilog10(t)+1)-t;

%p isprime(t*10^(ilog10(r)+1)+r)

%p end proc:

%p select(filter, [Res]); # _Robert Israel_, Jan 22 2019

%Y Cf. A056696, A108966.

%K base,easy,nonn

%O 1,2

%A _Jason Earls_, Jul 25 2005