

A061783


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


6



229, 239, 241, 257, 269, 271, 277, 281, 439, 443, 463, 467, 479, 499, 613, 641, 653, 661, 673, 677, 683, 691, 811, 823, 839, 863, 881, 20011, 20029, 20047, 20051, 20101, 20161, 20201, 20249, 20269, 20347, 20389, 20399, 20441, 20477, 20479, 20507
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OFFSET

1,1


COMMENTS

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


REFERENCES

O. Cira, F. Smarandache, Luhn prime numbers, 2014; http://www.gallup.unm.edu/~smarandache/ScArt7/CPLuhnPrimeNumbers.pdf


LINKS

Harry J. Smith and Chai Wah Wu, Table of n, a(n) for n = 1..50598, giving all terms below 9*10^6 (The first 1000 terms from Harry J. Smith)
Chai Wah Wu, 3010506 terms, 11MB zipped file of all terms below 10^9.


EXAMPLE

229 is a term since 229 is a prime and so is 229 + 922 = 1151.


MATHEMATICA

Select[Prime[Range[3000]], PrimeQ[#+FromDigits[Reverse[IntegerDigits[#]]]]&] (* Harvey P. Dale, Nov 27 2010 *)


PROG

(PARI) { n=0; forprime (p=2, 86843, x=p; r=0; while (x>0, d=x10*(x\10); x\=10; r=r*10 + d); if (isprime(p + r), write("b061783.txt", n++, " ", p)) ) } \\ Harry J. Smith, Jul 28 2009
(MAGMA) [NthPrime(n): n in [1..2400]  IsPrime(s) where s is NthPrime(n)+Seqint(Reverse(Intseq(NthPrime(n))))]; // Bruno Berselli, Aug 05 2013
(Python)
from sympy import isprime, prime
A061783 = [prime(n) for n in xrange(1, 10**5) if isprime(prime(n)+int(str(prime(n))[::1]))] # Chai Wah Wu, Aug 14 2014


CROSSREFS

Sequence in context: A091551 A033528 A086002 * A140017 A119711 A062589
Adjacent sequences: A061780 A061781 A061782 * A061784 A061785 A061786


KEYWORD

nonn,base,easy


AUTHOR

Amarnath Murthy, May 24 2001


EXTENSIONS

Corrected and extended by Patrick De Geest, May 26 2001


STATUS

approved



