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

1,1

Comments

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

Links

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

Example

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).

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 *)

Prog

(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

Crossrefs

Cf. A004086, A006567, A209871.

Sequence in context: A303918 A371378 A228625 * A214732 A088290 A209620

Adjacent sequences: A356944 A356945 A356946 * A356948 A356949 A356950

Keyword

nonn,base

Author

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

Status

approved