|
|
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
|
Matt Parker, 383 is cool, Numberphile series on YouTube, Feb. 15, 2017.
|
|
FORMULA
|
|
|
EXAMPLE
|
383 is a term because it is prime and it is the sum of prime 241 and its reverse 142.
|
|
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 *)
|
|
PROG
|
(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.
(End)
|
|
CROSSREFS
|
|
|
KEYWORD
|
base,nonn,changed
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|