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A342681
Primes which, when added to their reversals, produce palindromic primes.
1
241, 443, 613, 641, 811, 20011, 20047, 20051, 20101, 20161, 20201, 20347, 20441, 20477, 21001, 21157, 21211, 21377, 21467, 22027, 22031, 22147, 22171, 22247, 22367, 23017, 23021, 23131, 23357, 23417, 23447, 24007, 24121, 24151, 24407, 25031, 25111, 25117, 25121, 26021, 26107, 26111, 26417, 27011, 27407, 28001
OFFSET
1,1
COMMENTS
It appears that all terms have an odd number of digits. - Robert Israel, Mar 24 2021
LINKS
EXAMPLE
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.
MAPLE
revdigs:= proc(n) local i, L;
L:= convert(n, base, 10);
add(L[-i]*10^(i-1), i=1..nops(L))
end proc:
ispali:= proc(n) local L;
L:= convert(n, base, 10);
andmap(t -> L[t]=L[-t], [$1..nops(L)/2])
end proc:
filter:= proc(t) local r; r:= t + revdigs(t);
ispali(r) and isprime(r);
end proc:
select(filter, [seq(ithprime(i), i=1..10000)]); # Robert Israel, Mar 24 2021
MATHEMATICA
Select[Range[30000], PrimeQ[#] && PrimeQ[# + IntegerReverse[#]] && PalindromeQ[# + IntegerReverse[#]] &]
PROG
(PARI) isok(p) = my(q); isprime(p) && isprime(q=p+fromdigits(Vecrev(digits(p)))) && (q==fromdigits(Vecrev(digits(q)))); \\ Michel Marcus, Mar 18 2021
(Python)
from sympy import isprime, primerange
def ok(p):
t = p + int(str(p)[::-1]); strt = str(t)
return strt == strt[::-1] and isprime(t)
print([p for p in primerange(1, 28002) if ok(p)]) # Michael S. Branicky, Mar 18 2021
(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
CROSSREFS
Cf. A002385. Subsequence of A061783 (Luhn primes: primes p such that p + (p reversed) is also a prime).
Sequence in context: A325088 A321582 A137771 * A108831 A068706 A157961
KEYWORD
nonn,base
AUTHOR
Tanya Khovanova, Mar 18 2021
STATUS
approved