A161721 Primes p such that the reversal of p is prime and the product of p with its reversal is a palindrome.

2, 3, 11, 101, 1021, 1201, 111211, 112111, 1000211, 1010201, 1020101, 1101211, 1102111, 1111021, 1112011, 1120001, 1121011, 1201111, 10011101, 10012001, 10021001, 10100201, 10111001, 10200101, 11012011, 11021011, 11100121, 12100111

Offset: 1

Author

Tanya Khovanova, Jun 17 2009

Keywords

• base
• nonn

Comments

This sequence is a subsequence of A062936. If you multiply a member of this sequence by its reversal you get a number fixed under TITO algorithm (see A161594).

Conjecture: except for a(2) which equals 3, all terms can only be composed of the digits 0, 1 or 2. - Chai Wah Wu, Jan 07 2015

Conjecture: the digit 2 can only appear once in each term. - Robert G. Wilson v, Jan 07 2015

Number of terms less than 10^n: 2, 3, 4, 6, 6, 8, 18, 28, 37, 65, 97, 153, 230, 304, 414, 556, 756, 960, 1255, ... - Robert G. Wilson v, Jan 07 2015

A proper subset of A007500. - Robert G. Wilson v, Jan 07 2015

Examples

			1021 is a prime number, its reversal is 1201, which is also a prime. The product 1021*1201 = 1226221 is a palindrome.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1255 (first 97 terms from Chai Wah Wu)
• Tanya Khovanova, Turning Numbers Inside Out

Crossrefs

Cf. A161594, A161597, A161600.

Programs

Maple

rev := proc (n) local nn: nn := convert(n, base, 10): add(nn[j]*10^(nops(nn)-j), j = 1 .. nops(nn)) end proc: a := proc (n) local p: p := ithprime(n): if isprime(rev(p)) = true and rev(p*rev(p)) = p*rev(p) then p else end if end proc: seq(a(n), n = 1 .. 800000); # Emeric Deutsch, Jun 26 2009

Mathematica

rev[n_]:=FromDigits[Reverse[IntegerDigits[n]]]; t={}; Do[p=Prime[n]; If[PrimeQ[q=rev[p]] && rev[p*q]==p*q, AppendTo[t,p]], {n,8*10^5}]; t (* Jayanta Basu, May 11 2013 *)

Python

from sympy import isprime
A161721_list = [2]
for i in range(3,10**6,2):
    j = int(str(i)[::-1])
    if j == i:
        s = str(i**2)
        if s == s[::-1] and isprime(i):
            A161721_list.append(i)
    elif j > i:
        s = str(i*j)
        if s == s[::-1] and isprime(i) and isprime(j):
            A161721_list.extend([i,j])
A161721_list = sorted(A161721_list) # Chai Wah Wu, Jan 07 2015

Extensions

Edited by N. J. A. Sloane, Jun 23 2009

More terms from Emeric Deutsch, Jun 26 2009