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Palindromic primes using only digits 3 and 5.
1

%I #16 Dec 18 2015 03:10:28

%S 3,5,353,33533,35353,3353533,3553553,333535333,335333533,355353553,

%T 355555553,33335353333,33553335533,35533333553,35553535553,

%U 3335535355333,3335555555333,3353353533533,3353355533533,3355535355533,3533355533353,3533533353353

%N Palindromic primes using only digits 3 and 5.

%H Chai Wah Wu, <a href="/A138584/b138584.txt">Table of n, a(n) for n = 1..5382</a>

%p revdigs:= proc(n) option remember;

%p local b;

%p if n < 10 then return n fi;

%p b:= n mod 10;

%p b*10^ilog10(n) + procname((n-b)/10);

%p end proc:

%p A:= {3,5}:

%p B:= [0]:

%p for d from 2 to 20 do

%p if d::even then

%p B:= map(t -> (10*t+3,10*t+5), B);

%p A:= A union select(isprime, {seq(revdigs(b)+10^(d/2)*b,b=B)});

%p else

%p A:= A union select(isprime, {seq(seq(

%p revdigs(b)+i*10^((d-1)/2)+10^((d+1)/2)*b, i = [3,5]),b=B)});

%p fi

%p od:

%p sort(convert(A,list)); # _Robert Israel_, Dec 17 2015

%o (Python)

%o from itertools import product

%o from sympy import isprime

%o A138584_list = []

%o for l in range(17):

%o for d in product('35',repeat=l):

%o s = ''.join(d)

%o n = int(s+'3'+s[::-1])

%o if isprime(n):

%o A138584_list.append(n)

%o n += 2*10**l

%o if isprime(n):

%o A138584_list.append(n) # _Chai Wah Wu_, Dec 17 2015

%Y Cf. A020462.

%K nonn,base

%O 1,1

%A _Paul Curtz_, May 13 2008

%E More terms from _Arkadiusz Wesolowski_, Dec 31 2011