A375261 Smallest n-digit reversible prime with only prime digits.

2, 37, 337, 3257, 32233, 322573, 3222223, 32235223, 322222223, 3222222257, 32222232577, 322222232537, 3222222223333, 32222222332733, 322222222237537, 3222222222223373, 32222222222223353, 322222222222225333, 3222222222222222577, 32222222222222225573, 322222222222222233253

Offset: 1

Author

Jean-Marc Rebert, Aug 08 2024

Keywords

• base
• nonn

Comments

Differs from A177513(n) for n in A082705. - Robert Israel, May 11 2025

Links

• Robert Israel, Table of n, a(n) for n = 1..243

Crossrefs

Cf. A006567, A082705, A160748, A177513.

Programs

Maple

PD:= [2,3,5,7]:
g:= proc(n) local L,d,i,x,y;
  L:= convert(n,base,4); d:= nops(L);
  x:= add(PD[L[i]+1]*10^(i-1),i=1..d);
  y:= add(PD[L[-i]+1]*10^(i-1),i=1..d);
  if isprime(x) and isprime(y) then return x fi;
end proc:
f:= proc(d) local k,v;
  for k from 4^(d-1) do v:= g(k); if v <> NULL then return v fi od
end proc;
f(1):= 2:
map(f, [$1..30]); # Robert Israel, May 11 2025

Python

from sympy import isprime
from itertools import product
def a(n):
    if n == 1: return 2
    for first in "37":
        for rest in product("2357", repeat=n-1):
            s = first + "".join(rest)
            if isprime(t:=int(s)) and isprime(int(s[::-1])):
                return t
print([a(n) for n in range(1, 22)]) # Michael S. Branicky, Aug 08 2024

Formula

a(n) <= A177513(n) for n > 1.

If a(n) is not a palindrome, a(n) = A177513(n) for n > 1.