A157712 Smallest prime made up of 0's and prime(n) 1's (or 0 when no such prime exists).

11, 0, 101111, 11110111, 101111111111, 101101111111111, 101111111111111111, 1111111111111111111, 11111111111111111111111, 111110111111111111111111111111, 11111101111111111111111111111111

Offset: 1

Author

Lekraj Beedassy, Mar 04 2009

Keywords

• nonn
• base

Comments

Smallest prime with digit sum A000040(n) and using only 0's and 1's. Subsequence of A157709.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..168

Crossrefs

Cf. A054750.

Programs

Python

from _future_ import division
from itertools import combinations
from sympy import prime, isprime
def A157712(n):
    if n == 1:
        return 11
    if n == 2:
        return 0
    p = prime(n)
    l = p
    while True:
        for i in combinations(range(l),l-p):
            s = ['1']*l
            for x in i:
                s[x] = '0'
            q = int(''.join(s))
            if isprime(q):
                return q
        l += 1 # Chai Wah Wu, Nov 05 2015

Extensions

Extended by Ray Chandler, Mar 06 2009