A158214 Smallest palindromic prime made up of 0's and k 1's, where k = A007310(n), odd numbers not divisible by 3.

100111001, 110111011, 1110111110111, 10111101110111101, 100111111111111111001, 1111111111111111111, 11111111111111111111111, 10111111111101110111111111101, 1111110111111111111111110111111

Offset: 2

Author

Lekraj Beedassy, Mar 13 2009

Keywords

• nonn
• base

Comments

Smallest palindromic prime with digit sum A007310(n) and using only 0's and 1's.

Links

• Chai Wah Wu, Table of n, a(n) for n = 2..167

Crossrefs

Cf. A020449.

Programs

Python

from _future_ import division
from sympy.utilities.iterables import multiset_permutations
from sympy import isprime
A158214_list = []
for i in range(2,101):
    if i % 6 == 1 or i % 6 == 5:
        i2 = i//2
        l = i2
        flag = True
        while flag:
            dlist = '0'*(l-i2) + '1'*i2
            for d in multiset_permutations(dlist):
                s = ''.join(d)
                n = int(s+'1'+s[::-1])
                if isprime(n):
                    A158214_list.append(n)
                    flag = False
                    break
            else:
                l += 1 # Chai Wah Wu, Dec 17 2015