A342681 Primes which, when added to their reversals, produce palindromic primes.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Adjacent sequences: A342678 A342679 A342680 * A342682 A342683 A342684

Keyword

nonn,base

Author

Tanya Khovanova, Mar 18 2021

Status

approved