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 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified October 25 04:05 EDT 2020. Contains 338011 sequences. (Running on oeis4.)