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

1,1

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

Formula

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

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

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

Prog

(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

Crossrefs

Cf. A006567, A082705, A160748, A177513.

Sequence in context: A200911 A243101 A001569 * A383814 A373618 A092853

Adjacent sequences: A375258 A375259 A375260 * A375262 A375263 A375264

Keyword

base,nonn

Author

Jean-Marc Rebert, Aug 08 2024

Status

approved