A111382 Beginning with 3, least number such that concatenation of first n terms and its digit reversal both are primes.

3, 1, 1, 21, 11, 43, 47, 157, 753, 51, 917, 273, 2409, 703, 413, 3729, 1153, 6243, 8789, 2307, 4477, 137, 403, 10649, 4617, 4533, 6133, 4721, 877, 2469, 5967, 1557, 1047, 38931, 15533, 6877, 23987, 4767, 18049, 1463, 118333, 27897

Offset: 1

Author

Hans Havermann, Nov 08 2005

Keywords

• nonn
• base

Links

• Robert Israel, Table of n, a(n) for n = 1..160

Crossrefs

Cf. A113584.

Programs

Maple

rev:= proc(n) local L,i;
  L:= convert(n,base,10);
  add(L[-i]*10^(i-1),i=1..nops(L))
end proc;
R:= 3: X:= 3: XR:= 3:
for i from 2 to 50 do
  for x from 1 by 2 do
    d:= 1+ilog10(x);
    t:= X*10^(1+ilog10(x)) + x;
    if not isprime(t) then next fi;
    xr:= rev(x);
    tr:= XR+xr*10^(1+ilog10(XR));
    if isprime(tr) then break fi;
  od;
  X:= t; XR:= tr; R:= R,x;
od:
R; # Robert Israel, Aug 09 2023

Python

from itertools import count, islice
from gmpy2 import digits, is_prime, mpz
def agen(): # generator of terms
    s, r, an = "", "", 3
    while True:
        yield int(an)
        d = digits(an)
        s, r, k, sk = s+d, d[::-1]+r, 1, "1"
        while not is_prime(mpz(s+sk)) or not is_prime(mpz(sk[::-1]+r)):
            k += 2
            if k%10 == 5: k += 2
            sk = digits(k)
        an = k
print(list(islice(agen(), 42))) # Michael S. Branicky, Jan 02 2025