A375261 - OEIS

%I #23 May 12 2025 14:38:01

%S 2,37,337,3257,32233,322573,3222223,32235223,322222223,3222222257,

%T 32222232577,322222232537,3222222223333,32222222332733,

%U 322222222237537,3222222222223373,32222222222223353,322222222222225333,3222222222222222577,32222222222222225573,322222222222222233253

%N Smallest n-digit reversible prime with only prime digits.

%C Differs from A177513(n) for n in A082705. - _Robert Israel_, May 11 2025

%H Robert Israel, <a href="/A375261/b375261.txt">Table of n, a(n) for n = 1..243</a>

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

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

%p PD:= [2,3,5,7]:

%p g:= proc(n) local L,d,i,x,y;

%p   L:= convert(n,base,4); d:= nops(L);

%p   x:= add(PD[L[i]+1]*10^(i-1),i=1..d);

%p   y:= add(PD[L[-i]+1]*10^(i-1),i=1..d);

%p   if isprime(x) and isprime(y) then return x fi;

%p end proc:

%p f:= proc(d) local k,v;

%p   for k from 4^(d-1) do v:= g(k); if v <> NULL then return v fi od

%p end proc;

%p f(1):= 2:

%p map(f, [$1..30]); # _Robert Israel_, May 11 2025

%o (Python)

%o from sympy import isprime

%o from itertools import product

%o def a(n):

%o     if n == 1: return 2

%o     for first in "37":

%o         for rest in product("2357", repeat=n-1):

%o             s = first + "".join(rest)

%o             if isprime(t:=int(s)) and isprime(int(s[::-1])):

%o                 return t

%o print([a(n) for n in range(1, 22)]) # _Michael S. Branicky_, Aug 08 2024

%Y Cf. A006567, A082705, A160748, A177513.

%K base,nonn

%O 1,1

%A _Jean-Marc Rebert_, Aug 08 2024