A051835 Palindromic Sophie Germain primes.

2, 3, 5, 11, 131, 191, 12821, 14741, 19391, 19991, 36563, 38183, 93239, 96269, 1028201, 1074701, 1150511, 1178711, 1243421, 1281821, 1317131, 1333331, 1407041, 1456541, 1508051, 1532351, 1557551, 1598951, 1600061, 1609061

Offset: 1

Author

Warut Roonguthai Dec 11 1999

Keywords

• base
• nonn

Comments

p and 2p+1 are primes (cf. A005384) and p is a palindrome.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• H. Dubner, Palindromic Sophie Germain primes, Journal of Recreational Mathematics, Vol. 26, No. 1, pp. 38-41, 1994.

Crossrefs

Cf. A002385, A005384.

Programs

Maple

makepali:= proc(n, d) local L; # case with d odd
  L:= convert(n, base, 10);
  10^((d-1)/2)*n + add(L[i]*10^((d+1)/2-i), i=2..(d+1)/2)
end proc:
N:= 100: # for a(1)..a(N)
R:= 2,3,5,11: count:= 4:
for d from 3 by 2  while count < N do
  for i in [1,3,7,9] while count < N do
    for x from 0 to 10^((d-1)/2)-1 while count < N do
      y:= makepali(i*10^((d-1)/2)+x,d);
      if isprime(y) and isprime(2*y+1) then
        R:= R, y;
        count:= count+1;
       fi
od od od:
R; # Robert Israel, Nov 22 2020

Mathematica

Select[Prime[Range[125000]],PrimeQ[2#+1]&&PalindromeQ[#]&] (* Harvey P. Dale, Nov 21 2021 *)