A330202 Palindromic primes p in base 10 such that 6*p+1 is also a palindromic prime in base 10.

131, 12130303121, 131302030203131, 12130313131303121, 13020303130302031, 13030212121203031, 1213130303030313121, 1312131302031312131, 121312031202130213121, 130212020303020212031, 130212121303121212031, 130312121202121213031, 12020312021312021302021, 12121212031213021212121

Offset

1,1

Comments

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).

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10008

Formula

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

Prog

(Python)
from sympy import isprime
A330202_list = []
for i in range(2**20):
    s = bin(i)[2:]
    s += s[-2::-1]
    p = int(s) + int('02'*(len(s)//2)+'0')
    q = 6*p+1
    t = str(q)
    if t == t[::-1] and isprime(p) and isprime(q):
        A330202_list.append(p)

Crossrefs

Cf. A002113, A002385, A321210.

Sequence in context: A222876 A267720 A263299 * A243832 A331909 A001295

Adjacent sequences: A330199 A330200 A330201 * A330203 A330204 A330205

Keyword

nonn,base

Author

Chai Wah Wu, Dec 05 2019

Status

approved