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

Author

Shyam Sunder Gupta, Jul 20 2002

Keywords

• base
• nonn

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

Examples

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

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.

Crossrefs

Cf. A004086 (reverse), A004087 (primes reversed), A056964 (reverse & add), A061783 (Luhn primes), A086002 (similar, using "rotate" instead of "reverse").

Programs

Mathematica

f@n_:=(Select[# + IntegerReverse[#] & /@ Prime[Range[n]], PrimeQ@# && # <= Prime[n] &] // Union); f@3000 (* Harvey P. Dale, Jul 18 2018; corrected by Hans Rudolf Widmer, Aug 15 2024 *)

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. - M. F. Hasler, Sep 26 2019

PARI

A072385=Set(apply(A056964, A061783)) \\ with, e.g.: A061783=select(is_A061783(p)={isprime(A056964(p))&&isprime(p)}, primes(8713)) - M. F. Hasler, Sep 26 2019

Formula

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

Extensions

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