cp's OEIS Frontend

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

%I A161721 #38 Feb 19 2025 17:31:18
%S A161721 2,3,11,101,1021,1201,111211,112111,1000211,1010201,1020101,1101211,
%T A161721 1102111,1111021,1112011,1120001,1121011,1201111,10011101,10012001,
%U A161721 10021001,10100201,10111001,10200101,11012011,11021011,11100121,12100111
%N A161721 Primes p such that the reversal of p is prime and the product of p with its reversal is a palindrome.
%C A161721 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).
%C A161721 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
%C A161721 Conjecture: the digit 2 can only appear once in each term. - _Robert G. Wilson v_, Jan 07 2015
%C A161721 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
%C A161721 A proper subset of A007500. - _Robert G. Wilson v_, Jan 07 2015
%H A161721 Robert G. Wilson v, <a href="/A161721/b161721.txt">Table of n, a(n) for n = 1..1255</a> (first 97 terms from Chai Wah Wu)
%H A161721 Tanya Khovanova, <a href="http://blog.tanyakhovanova.com/?p=144">Turning Numbers Inside Out</a>
%e A161721 1021 is a prime number, its reversal is 1201, which is also a prime. The product 1021*1201 = 1226221 is a palindrome.
%p A161721 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
%t A161721 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 *)
%o A161721 (Python)
%o A161721 from sympy import isprime
%o A161721 A161721_list = [2]
%o A161721 for i in range(3,10**6,2):
%o A161721     j = int(str(i)[::-1])
%o A161721     if j == i:
%o A161721         s = str(i**2)
%o A161721         if s == s[::-1] and isprime(i):
%o A161721             A161721_list.append(i)
%o A161721     elif j > i:
%o A161721         s = str(i*j)
%o A161721         if s == s[::-1] and isprime(i) and isprime(j):
%o A161721             A161721_list.extend([i,j])
%o A161721 A161721_list = sorted(A161721_list) # _Chai Wah Wu_, Jan 07 2015
%Y A161721 Cf. A161594, A161597, A161600.
%K A161721 base,nonn
%O A161721 1,1
%A A161721 _Tanya Khovanova_, Jun 17 2009
%E A161721 Edited by _N. J. A. Sloane_, Jun 23 2009
%E A161721 More terms from _Emeric Deutsch_, Jun 26 2009