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A061783 Luhn primes: primes p such that p + (p reversed) is also a prime.

%I A061783 #60 Dec 08 2024 20:41:50
%S A061783 229,239,241,257,269,271,277,281,439,443,463,467,479,499,613,641,653,
%T A061783 661,673,677,683,691,811,823,839,863,881,20011,20029,20047,20051,
%U A061783 20101,20161,20201,20249,20269,20347,20389,20399,20441,20477,20479,20507
%N A061783 Luhn primes: primes p such that p + (p reversed) is also a prime.
%C A061783 a(n) has an odd number of digits, as otherwise a(n) + reverse(a(n)) is a multiple of 11. For a(n) > 10, a(n) is prime and thus odd, and therefore the first digit of a(n) is even as otherwise a(n) + reverse(a(n)) is even and composite. - _Chai Wah Wu_, Aug 19 2015
%C A061783 See A072385 for the resulting primes p + reverse(p) = A056964(p). - _M. F. Hasler_, Sep 26 2019
%C A061783 Named by Cira and Smarandache (2014) after Norman Luhn, who noted the property of the prime 229 on the Prime Curios! website. - _Amiram Eldar_, Jun 05 2021
%H A061783 Harry J. Smith and Chai Wah Wu, <a href="/A061783/b061783.txt">Table of n, a(n) for n = 1..50598</a>, giving all terms below 9*10^6 (The first 1000 terms from Harry J. Smith)
%H A061783 Octavian Cira and Florian Smarandache, <a href="https://uav.ro/applications/se/journal/index.php/TAMCS/article/view/112/90">Luhn prime numbers</a>, Theory and Applications of Mathematics & Computer Science, Vol. 5, No. 1 (2015), pp. 29-36; <a href="http://fs.unm.edu/ScArt/LuhnPrimeNumbers.pdf">preprint</a>, 2014.
%H A061783 G. L. Honaker, Jr. and Chris Caldwell, eds., <a href="https://primes.utm.edu/curios/page.php?curio_id=2522">229</a>, Prime Curios!, November 19, 2001.
%H A061783 Chai Wah Wu, <a href="/A061783/a061783-big.zip">3010506 terms</a>, 11MB zipped file of all terms below 10^9.
%e A061783 229 is a term since 229 is a prime and so is 229 + 922 = 1151.
%t A061783 Select[Prime[Range[3000]],PrimeQ[#+FromDigits[Reverse[IntegerDigits[#]]]]&] (* _Harvey P. Dale_, Nov 27 2010 *)
%o A061783 (PARI) isok(p) = { isprime(p) && isprime(p + fromdigits(Vecrev(digits(p)))) } \\ _Harry J. Smith_, Jul 28 2009
%o A061783 (PARI) select( is_A061783(p)=isprime(A056964(p)) && isprime(p), primes(8713)) \\  A056964(p)=p+fromdigits(Vecrev(digits(p))). There is no term with 4 digits or starting with an odd digit, i.e., no candidate between prime(168) = 997 and prime(2263) = 20011. Using primes up to prime(8713) = 89989 ensures the list of 5-digit terms is complete. - _M. F. Hasler_, Sep 26 2019
%o A061783 (Magma) [NthPrime(n): n in [1..2400] | IsPrime(s) where s is NthPrime(n)+Seqint(Reverse(Intseq(NthPrime(n))))]; // _Bruno Berselli_, Aug 05 2013
%o A061783 (Python)
%o A061783 from sympy import isprime, prime
%o A061783 A061783 = [prime(n) for n in range(1,10**5) if isprime(prime(n)+int(str(prime(n))[::-1]))] # _Chai Wah Wu_, Aug 14 2014
%Y A061783 Cf. A004086 (reverse), A004087 (primes reversed), A056964 (reverse & add), A072385, A086002 (similar, using "rotate" instead of "reverse").
%K A061783 nonn,base,easy
%O A061783 1,1
%A A061783 _Amarnath Murthy_, May 24 2001
%E A061783 Corrected and extended by _Patrick De Geest_, May 26 2001
%E A061783 Cross-references added by _M. F. Hasler_, Sep 26 2019