A356947 Emirps p such that p == 1 (mod s) and R(p) == 1 (mod s), where R(p) is the digit reversal of p and s the sum of digits of p.

1021, 1031, 1201, 1259, 1301, 9521, 10253, 10711, 11071, 11161, 11243, 11701, 12113, 12241, 14221, 15907, 16111, 16481, 17011, 17491, 18461, 19471, 30757, 31121, 34211, 35201, 70951, 71347, 71569, 72337, 73327, 74317, 75703, 96517, 100621, 101611, 101701, 102061, 102913, 103141, 105211, 106661

Offset: 1

Author

J. M. Bergot and Robert Israel, Sep 05 2022

Keywords

• nonn
• base

Comments

Emirps p such that p and its digit reversal are quasi-Niven numbers.

Examples

			a(3) = 1201 is a term because it and its digit reversal 1021 are distinct primes with sum of digits 4, and 1201 == 1021 == 1 (mod 4).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A004086, A006567, A209871.

Programs

Maple

filter:= proc(n) local L,i,r,s;
  if not isprime(n) then return false fi;
  L:= convert(n,base,10);
  r:= add(L[-i]*10^(i-1),i=1..nops(L));
  if r = n or not isprime(r) then return false fi;
  s:= convert(L,`+`);
  n mod s = 1 and r mod s = 1
end proc:
select(filter, [seq(i,i=13 .. 200000, 2)]);

Mathematica

Select[Range[110000], (r = IntegerReverse[#]) != # && PrimeQ[#] && PrimeQ[r] && Divisible[# - 1, (s = Plus @@ IntegerDigits[#])] && Divisible[r - 1, s] &] (* Amiram Eldar, Sep 06 2022 *)

Python

from sympy import isprime
def ok(n):
    strn = str(n)
    R, s = int(strn[::-1]), sum(map(int, strn))
    return n != R and n%s == 1 and R%s == 1 and isprime(n) and isprime(R)
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Sep 06 2022