A061783 -id:A061783 - cp's OEIS frontend

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

Tanya Khovanova, Mar 18 2021

It appears that all terms have an odd number of digits. - Robert Israel, Mar 24 2021

			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.

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

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

[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

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

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

isok(p) = my(q); isprime(p) && isprime(q=p+fromdigits(Vecrev(digits(p)))) && (q==fromdigits(Vecrev(digits(q)))); \\ Michel Marcus, Mar 18 2021

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

A350575 Squarefree numbers k such that k + (k reversed) is also squarefree.

Original entry on oeis.org

1, 3, 5, 7, 10, 11, 14, 15, 19, 21, 23, 30, 33, 34, 37, 41, 42, 43, 46, 51, 55, 58, 59, 61, 67, 69, 70, 73, 77, 78, 82, 85, 86, 87, 89, 91, 94, 95, 101, 102, 105, 106, 109, 111, 115, 118, 119, 130, 131, 134, 138, 139, 141, 142, 146, 149, 151, 155, 158, 159, 161, 166, 170, 174, 178, 181, 182, 185, 190, 191, 194, 195, 199

Offset: 1

Jean-François Alcover, Jan 07 2022

This is to squarefree numbers what A061783 is to primes.

			14 is a term since it's squarefree and so is 14 + 41 = 55.

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

Cf. A004086, A005117, A056964, A061783.

R:= n-> (s-> parse(cat(s[-i]$i=1..length(s))))(""||n):
q:= n-> andmap(numtheory[issqrfree], [n, n+R(n)]):
select(q, [$1..200])[];  # Alois P. Heinz, Jan 07 2022

okQ[n_] := SquareFreeQ[n] && SquareFreeQ[n + IntegerReverse[n]];
Select[Range[200], okQ]

isok(m) = issquarefree(m) && issquarefree(m+fromdigits(Vecrev(digits(m)))); \\ Michel Marcus, Jan 07 2022

from sympy.ntheory.factor_ import core
def squarefree(n): return core(n, 2) == n
def ok(n): return squarefree(n) and squarefree(n + int(str(n)[::-1]))
print([k for k in range(1, 200) if ok(k)]) # Michael S. Branicky, Jan 07 2022

cp's OEIS Frontend

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

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