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A051835 Palindromic Sophie Germain primes.

%I A051835 #10 Nov 21 2021 19:05:11
%S A051835 2,3,5,11,131,191,12821,14741,19391,19991,36563,38183,93239,96269,
%T A051835 1028201,1074701,1150511,1178711,1243421,1281821,1317131,1333331,
%U A051835 1407041,1456541,1508051,1532351,1557551,1598951,1600061,1609061
%N A051835 Palindromic Sophie Germain primes.
%C A051835 p and 2p+1 are primes (cf. A005384) and p is a palindrome.
%H A051835 Robert Israel, <a href="/A051835/b051835.txt">Table of n, a(n) for n = 1..10000</a>
%H A051835 H. Dubner, <a href="http://ksc9.th.com/warut/dubner.html">Palindromic Sophie Germain primes</a>, Journal of Recreational Mathematics, Vol. 26, No. 1, pp. 38-41, 1994.
%p A051835 makepali:= proc(n, d) local L; # case with d odd
%p A051835   L:= convert(n, base, 10);
%p A051835   10^((d-1)/2)*n + add(L[i]*10^((d+1)/2-i), i=2..(d+1)/2)
%p A051835 end proc:
%p A051835 N:= 100: # for a(1)..a(N)
%p A051835 R:= 2,3,5,11: count:= 4:
%p A051835 for d from 3 by 2  while count < N do
%p A051835   for i in [1,3,7,9] while count < N do
%p A051835     for x from 0 to 10^((d-1)/2)-1 while count < N do
%p A051835       y:= makepali(i*10^((d-1)/2)+x,d);
%p A051835       if isprime(y) and isprime(2*y+1) then
%p A051835         R:= R, y;
%p A051835         count:= count+1;
%p A051835        fi
%p A051835 od od od:
%p A051835 R; # _Robert Israel_, Nov 22 2020
%t A051835 Select[Prime[Range[125000]],PrimeQ[2#+1]&&PalindromeQ[#]&] (* _Harvey P. Dale_, Nov 21 2021 *)
%Y A051835 Cf. A002385, A005384.
%K A051835 base,nonn
%O A051835 1,1
%A A051835 _Warut Roonguthai_ Dec 11 1999