

A072385


Primes which can be represented as the sum of a prime and its reverse.


2



383, 443, 463, 787, 827, 887, 929, 1009, 1049, 1069, 1151, 1171, 1231, 1373, 1453, 1493, 1777, 30203, 30403, 31013, 32213, 32413, 32423, 33023, 33223, 34033, 34843, 35053, 36263, 36653, 37273, 37463, 37663, 38083, 38273, 38873, 39293, 39883
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OFFSET

1,1


COMMENTS

This set is the image under the "reverse and add" operation (A056964) of the Luhn primes A061783 (which remain prime under that operation). Those have always an odd number of digits, and start with an even digit. Therefore this sequence has its terms in intervals [3,20]*100^k with k = 1, 2, 3....  M. F. Hasler, Sep 26 2019


LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..253 from M. F. Hasler)
Matt Parker, 383 is cool, Numberphile series on YouTube, Feb. 15, 2017.


FORMULA

a(n) = A056964(A061783(n)).  M. F. Hasler, Sep 26 2019


EXAMPLE

383 is a term because it is prime and it is the sum of prime 241 and its reverse 142.


MATHEMATICA

Select[#+IntegerReverse[#]&/@Prime[Range[3000]], PrimeQ]//Union (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 18 2018 *)


PROG

From M. F. Hasler, Sep 26 2019: (Start)
(PARI) is_A072385(p)={isprime(p)&&forprime(q=p\10, p*9\10, A056964(q)==p&&return(1))} \\ A056964(n)=n+fromdigits(Vecrev(digits(n))). It is much faster to produce the terms as shown below, rather than to "select" them from a range of primes.
A072385=Set(apply(A056964, A061783)) \\ with, e.g.: A061783=select(is_A061783(p)={isprime(A056964(p))&&isprime(p)}, primes(8713))
(End)


CROSSREFS

Cf. A004086 (reverse), A004087 (primes reversed), A056964 (reverse & add), A061783 (Luhn primes), A086002 (similar, using "rotate" instead of "reverse").
Sequence in context: A214896 A204861 A015861 * A045122 A064721 A252060
Adjacent sequences: A072382 A072383 A072384 * A072386 A072387 A072388


KEYWORD

base,nonn


AUTHOR

Shyam Sunder Gupta, Jul 20 2002


EXTENSIONS

Crossreferences added by M. F. Hasler, Sep 26 2019


STATUS

approved



