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A061783 Luhn primes: primes p such that p + (p reversed) is also a prime. 9
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 (list; graph; refs; listen; history; text; internal format)
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

See A072385 for the resulting primes p + reverse(p) = A056964(p). - M. F. Hasler, Sep 26 2019

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)

O. Cira, F. Smarandache, Luhn prime numbers, 2014.

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=x-10*(x\10); x\=10; r=r*10 + d); if (isprime(p + r), write("b061783.txt", n++, " ", p)) ) } \\ Harry J. Smith, Jul 28 2009

(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

(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 range(1, 10**5) if isprime(prime(n)+int(str(prime(n))[::-1]))] # Chai Wah Wu, Aug 14 2014

CROSSREFS

Cf. A004086 (reverse), A004087 (primes reversed), A056964 (reverse & add), A072385, A086002 (similar, using "rotate" instead of "reverse").

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

Cross-references added by M. F. Hasler, Sep 26 2019

STATUS

approved

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Last modified July 13 08:26 EDT 2020. Contains 335685 sequences. (Running on oeis4.)