A330202 - OEIS

%I #16 Jul 29 2023 06:43:44

%S 131,12130303121,131302030203131,12130313131303121,13020303130302031,

%T 13030212121203031,1213130303030313121,1312131302031312131,

%U 121312031202130213121,130212020303020212031,130212121303121212031,130312121202121213031,12020312021312021302021,12121212031213021212121

%N Palindromic primes p in base 10 such that 6*p+1 is also a palindromic prime in base 10.

%C Each term starts with either 12 or 13. If a term is written as a0a1a2...a2a1a0, then a_i is either 0 or 1 when i is even and a_i is either 2 or 3 when i is odd (see A321210).

%H Chai Wah Wu, <a href="/A330202/b330202.txt">Table of n, a(n) for n = 1..10008</a>

%F a(n) = (A321210(n)-1)/6.

%o (Python)

%o from sympy import isprime

%o A330202_list = []

%o for i in range(2**20):

%o     s = bin(i)[2:]

%o     s += s[-2::-1]

%o     p = int(s) + int('02'*(len(s)//2)+'0')

%o     q = 6*p+1

%o     t = str(q)

%o     if t == t[::-1] and isprime(p) and isprime(q):

%o         A330202_list.append(p)

%Y Cf. A002113, A002385, A321210.

%K nonn,base

%O 1,1

%A _Chai Wah Wu_, Dec 05 2019