A051835 -id:A051835 - cp's OEIS frontend

A082520 Palindromic Sophie Germain primes: both p and 2p+1 are palindromic primes.

2, 3, 5, 191, 19391, 38183, 1508051, 1609061, 1628261, 3717173, 3916193, 161535161, 161838161, 170646071, 172747271, 182949281, 190909091, 352909253, 354848453, 360818063, 364636463, 15052625051, 15150805151, 15253635251

Offset: 1

Lekraj Beedassy, Apr 30 2003

Subsequence of A051835 (intersection of A002385 and A005384).

			3916193 is in the sequence because both 3916193 and 2*3916193 + 1 = 7832387 are palindromic primes.

H. Dubner, "Palindromic Sophie Germain primes", Journal of Recreational Mathematics, Vol. 26(1):38-41 1994 Baywood Inc. NY

Dmitry Petukhov, Table of n, a(n) for n = 1..804 (terms up to 10^15).
H. Dubner, Palindromic Sophie Germain Primes

Cf. A002385, A005384, A051835.

The associated primes are listed in A082565.

Select[Prime@Range@1000000,PalindromeQ@#&&PalindromeQ[2#+1]&&PrimeQ[2#+1]&] (* Giorgos Kalogeropoulos, May 14 2021 *)

A118573 Sophie Germain primes for which the reversal is also a Sophie Germain prime.

Original entry on oeis.org

2, 3, 5, 11, 131, 191, 359, 953, 1229, 1583, 3851, 9221, 10061, 11579, 11939, 12119, 12821, 13619, 14081, 14741, 14939, 15791, 15803, 16001, 16883, 18041, 19163, 19391, 19751, 19991, 30851, 31859, 32633, 33623, 33809, 35993, 36191, 36563

Offset: 1

Luc Stevens (lms022(AT)yahoo.com), May 07 2006

{k such that k is in A005384 and A004086(k) is in A005384}. - Jonathan Vos Post, Apr 18 2008

			359 is in the sequence because it is a Sophie Germain prime and its reversal 953 is also a Sophie Germain prime.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A004086, A005384.

A051835 is a subsequence.

Select[Prime[Range[10000]], PrimeQ[2*# + 1] && PrimeQ[FromDigits[Reverse[ IntegerDigits[ # ]]]] && PrimeQ[2*FromDigits[Reverse[IntegerDigits[ # ]]] + 1] &] (* Stefan Steinerberger, May 18 2008 *)
fQ[n_] := (rp = FromDigits@ Reverse@ IntegerDigits@n; PrimeQ[2n + 1] && PrimeQ[rp] && PrimeQ[2rp + 1]); Select[Prime@ Range@4093, fQ@# &] (* Robert G. Wilson v, May 09 2006 *)

More terms from Robert G. Wilson v and Adam Panagos (adam.panagos(AT)gmail.com), May 09 2006

Edited by N. J. A. Sloane, Mar 02 2009 at the suggestion of R. J. Mathar

cp's OEIS Frontend

A082520 Palindromic Sophie Germain primes: both p and 2p+1 are palindromic primes.

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