A088269 Palindromic primes that yield a prime when sandwiched between two 1's. (Prefixing and suffixing a 1 on both sides yields another palindromic prime.)

3, 5, 131, 383, 797, 11411, 16061, 16361, 19391, 33533, 36263, 73037, 75557, 79397, 1074701, 1126211, 1145411, 1175711, 1221221, 1243421, 1287821, 1303031, 1311131, 1328231, 1363631, 1489841, 1579751, 1600061, 1707071, 1748471

Offset: 1

Author

Amarnath Murthy, Sep 28 2003

Keywords

• base
• nonn

Comments

There are two 1-digit terms, three 3-digit terms, nine 5-digit terms, 93 7-digit terms, 241 9-digit terms and no terms with an even number of digits. - Zak Seidov, Feb 23 2005

Examples

			Take palindromic primes (A002385) and see whether inserting them between two digits '1' again yields a prime:
Insert a(1) = 3 between the digits of 11 to get 131, a prime.
Insert a(2) = 5 between the digits of 11 to get 151, a prime.
Inserting 11 between two '1's yields 1111 = 11 * 101, not a prime.
Insert a(3) = 131 between the digits of 11 to get 11311, a prime.
Insert a(10) = 33533 between the digits of 11 to get 1335331, a prime, etc.
797 is a term as 17971 is also a prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A088270, A088271, A088272.

Cf. A002385.

Programs

Mathematica

Do[If[PrimeQ[n] && Reverse[IntegerDigits[n]] == IntegerDigits[n] && PrimeQ[ToExpression["1" <> ToString[n*10+1]]], Print[n]], {n, 1, 2*10^6}] (* Ryan Propper, Jul 09 2005 *)
palsQ[n_]:=Module[{idn=IntegerDigits[n],idn1},idn1=Join[{1},idn,{1}]; idn==Reverse[idn]&&idn1==Reverse[idn1]&&PrimeQ[FromDigits[idn1]]]; Select[Prime[Range[150000]],palsQ] (* Harvey P. Dale, Jan 04 2012 *)

PARI

is_A088269(n)={isprime(n)&&(n=digits(n))==Vecrev(n)&&isprime(fromdigits(concat([1,n,1])))} \\ M. F. Hasler, Nov 19 2018

Extensions

a(6)-a(30) from Ryan Propper, Jul 09 2005

Entry revised by N. J. A. Sloane, Apr 29 2007

Edited by M. F. Hasler, Nov 19 2018