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

1,1

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.

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 *)

Crossrefs

Cf. A002385, A005384.

Sequence in context: A117701 A056163 A118573 * A075883 A195815 A327428

Adjacent sequences: A051832 A051833 A051834 * A051836 A051837 A051838

Keyword

base,nonn

Author

Warut Roonguthai Dec 11 1999

Status

approved