A072385 Primes which can be represented as the sum of a prime and its reverse.

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

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

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

Status

approved