%I #20 Sep 08 2022 08:46:26

%S 241,443,613,641,811,20011,20047,20051,20101,20161,20201,20347,20441,

%T 20477,21001,21157,21211,21377,21467,22027,22031,22147,22171,22247,

%U 22367,23017,23021,23131,23357,23417,23447,24007,24121,24151,24407,25031,25111,25117,25121,26021,26107,26111,26417,27011,27407,28001

%N Primes which, when added to their reversals, produce palindromic primes.

%C It appears that all terms have an odd number of digits. - _Robert Israel_, Mar 24 2021

%H Robert Israel, <a href="/A342681/b342681.txt">Table of n, a(n) for n = 1..10000</a>

%e 241 is a prime number. The sum with its reverse is 383 = 241+142, which is a palindromic prime. Thus, 241 is in this sequence.

%p revdigs:= proc(n) local i,L;

%p L:= convert(n,base,10);

%p add(L[-i]*10^(i-1),i=1..nops(L))

%p end proc:

%p ispali:= proc(n) local L;

%p L:= convert(n,base,10);

%p andmap(t -> L[t]=L[-t], [$1..nops(L)/2])

%p end proc:

%p filter:= proc(t) local r; r:= t + revdigs(t);

%p ispali(r) and isprime(r);

%p end proc:

%p select(filter, [seq(ithprime(i),i=1..10000)]); # _Robert Israel_, Mar 24 2021

%t Select[Range[30000], PrimeQ[#] && PrimeQ[# + IntegerReverse[#]] && PalindromeQ[# + IntegerReverse[#]] &]

%o (PARI) isok(p) = my(q); isprime(p) && isprime(q=p+fromdigits(Vecrev(digits(p)))) && (q==fromdigits(Vecrev(digits(q)))); \\ _Michel Marcus_, Mar 18 2021

%o (Python)

%o from sympy import isprime, primerange

%o def ok(p):

%o t = p + int(str(p)[::-1]); strt = str(t)

%o return strt == strt[::-1] and isprime(t)

%o print([p for p in primerange(1, 28002) if ok(p)]) # _Michael S. Branicky_, Mar 18 2021

%o (Magma) [p: p in PrimesUpTo(10^6) | IsPrime(t) and Intseq(t) eq Reverse(Intseq(t)) where t is p+Seqint(Reverse(Intseq(p)))]; // _Bruno Berselli_, Mar 23 2021

%Y Cf. A002385. Subsequence of A061783 (Luhn primes: primes p such that p + (p reversed) is also a prime).

%K nonn,base

%O 1,1

%A _Tanya Khovanova_, Mar 18 2021